Answer: Here we compare [conversion] to laws of theft and damages. All agree that they require three judges.

R. Yochanan here explicitly holds in the Yerushalmi that if two judged, the verdict is invalid.

Question: How can we accept converts [nowadays]? We require expert [judges]!

Answer: We are Sheluchim [of expert judges from long ago], like it connotes also in Gitin 88b. (We coerce to give Gitin in Bavel. We are Sheluchim of expert judges in Eretz Yisrael, just like we are their Sheluchim to judge cases of admissions and loans.)

Just like they (experts) were concerned for people being deterred from lending [if they will not be able to bring the borrower to Beis Din, therefore they authorized judges to judge such cases in Chutz la'Aretz], they were concerned for people being unable to convert.

Explanation (R. Tam): This is only if we know that he was initially a Nochri. If we do not know, he is believed due to a Migo. If he wanted, he could have said "I am a Yisrael."

He is believed to say so, like it connotes in Pesachim (3b) regarding the Nochri who used to go and eat Korban Pesach in Yerushalayim. (They did not require proof that he is a Yisrael.)

Suggestion: Perhaps there is different, for they relied on the majority [of those who came to Yerushalayim], who were Yisre'elim.

Rejection: Also everywhere, the majority of those who come to us in the guise of Yisre'elim are Yisre'elim!

Support: In our Sugya, R. Yehudah said to him "you are not believed to disqualify your child." The man himself would have been Kosher, but [through his admission that he converted by himself], he established himself to be forbidden [a Nochri].

However, if he had Bi'ah with a Bas Kohen, he did not disqualify her, like I explained above (25b DH Leisa).

Suggestion: We can bring another support from above (45a). Amora'im advised [the son of a Nochri from a Bas Yisrael] to exile himself [to where he is not recognized, and he will be able to marry people of proper lineage. This implies that we do not require a proof that he is a Yisrael!]

Rejection: Perhaps they would check only that he is a Yisrael, but they would not check his family.

Explanation: [The verse teaches only that in Eretz Yisrael,] we accept converts.

Implied question: This is Chovas ha'Guf (it does not depend on the land. Such Mitzvos apply even in Chutz la'Aretz!)

Answer #1: Even so, we need a source to include Chutz la'Aretz, since it says ba'Aretz.

Support: We find like this in Kidushin (38b) regarding sending slaves free [in Yovel] and cancellation of loans [in Shemitah].

Answer #2: In Eretz Yisrael we are not concerned lest they retract [and decide to live like Nochrim again], due to the greatness of Eretz Yisrael. (One would think that we do not accept converts in Chutz la'Aretz, due to concern lest they retract.)

Alternate text: Some texts say "one might have thought that we believe them", i.e. they are believed [only] like Ed mi'Pi Ed (one who testified what another witness said, which is not accepted. The verse teaches that they are believed like proper witnesses.)

Explanation: He asked if he has witnesses that he converted by himself.

Question: If we require three for conversion only l'Chatchilah, but b'Di'eved one is Kosher, if so (that he has witnesses), the conversion was not by himself! (It was in front of two, which suffices b'Di'eved. Zera Yitzchak - Tosfos said above (45b DH Mi) that acceptance of Mitzvos must be in front of three, even b'Di'eved. Here he discusses whether the Tevilah must be in front of three.)

Explanation: This is only regarding matters in which he establishes himself to be forbidden. However, if he had Bi'ah with a Bas Kohen, he did not disqualify her, like I explained above (25b DH Leisa).

Question: What is the case? If his wife was a Nochris, in any case (whether he is a Yisrael or a Nochri), his children are forbidden, for [your child from a Nochris] is not called your child, rather, her child!

If his wife was a Yisraelis, in any case his children are Kosher, for we hold that the child of a Nochris who had Bi'ah with a Bas Yisrael is Kosher!

Suggestion: Granted, the child is not a Mamzer, but he is blemished (forbidden to Kehunah).

Question: Also now that he is not believed, the children are blemished, for R. Yehudah holds (Kidushin 77a) that the daughter of a male convert is like the daughter of a Chalal (she is a Chalalah)!

Answer: R. Yehudah holds that the child of a Nochris who had Bi'ah with a Bas Yisrael is a Mamzer.

Source: In Sanhedrin (53a), we say that R. Yehudah holds like R. Akiva, who says that Kedushin does not take effect with Chayavei Lavin.

Explanation #1 (R. Eliyahu of Paris): We learn from "Ben ha'Senu'ah Yakir." (He will inform people that his mother's marriage was hated, i.e. forbidden.) The Yerushalmi in Kidushin connotes like this.

Question: The Bavli connotes unlike this. It says "just like one is believed to say "this son is my firstborn..." This connotes that we learn from there!

Explanation #2: Some say that R. Yehudah understands the verse to teach that one is believed to say "this son is my firstborn" even if there are older sons [that his wife conceived during their marriage]. When he says that the younger son is his firstborn, if so, the first is a Mamzer!

Inference: He is believed to disqualify him. Likewise, he is believed to say that he is a Ben Gerushah.

Explanation: He is believed about himself because he established himself to be forbidden. (This works like an admission, or like a vow to conduct as if he is forbidden.)

Explanation (Ri): He means that you are believed to disqualify your children, i.e. when he has only children, but not grandchildren;

You are not believed to disqualify your grandchildren, i.e. when he has grandchildren he is not believed to disqualify even his children. It is unreasonable that his children are Pesulim, and his grandchildren are Kesherim!

Support: Below, we say that one is not believed about his big son. We explain that this is when he (the son) has children. This implies that he is not believed also about his son.

Pesak: This implies that the Halachah follows R. Yehudah. One is believed even to disqualify even his children. It is only because a Nochri cannot testify that he cannot disqualify them.

This is unlike R. Tam, who says that the Halachah follows R. Yehudah only when he disqualifies others through identifying the Bechor, but not when it is not through identifying the Bechor.

Support (for Tosfos' Pesak): Also the She'altos in Vayera derives from our Sugya that the Halachah follows R. Yehudah in every case.

Inference: The circumcision precedes the Tevilah, like we say "he is not a convert until he circumcises and immerses."

Question: We say below (78a) that if a pregnant woman converted, her son does not require Tevilah! (His mother's Tevilah helped for him. Her body was not a Chatzitzah, for he grows in it. This is before Milah!)

Answer (Ri): There is different, for he was not yet ready for Milah.

Implied question: The Torah did not explicitly write that a Nidah must immerse! (What is the source?)

Answer #1 (Rav Yehudah Gaon): We learn from a Kal va'Chomer from what she touched, which requires Tevilah. All the more so she herself requires Tevilah!

Answer #2 (R. Tam): We learn from the Drashah in Avodah Zarah (75b) "Ach b'Mei Nidah Yischata" - water in which a Nidah immerses. This is [a Mikveh of] 40 Sa'im.

Answer #3 (R. Yitzchak): In Shabbos (64) we learn from "Tihyeh Nidasah" - she is a Nidah until she enters water.

Observation: In our entire Sugya, it implies that a slave requires Tevilah when he is freed. His initial Tevilah (when he became an Eved Kena'ani) does not suffice.

Question: In Gitin (40a), we say that if one wrote a document of Kidushin to his Shifchah, and said "go out (free) with it, and be Mekudeshes [to me] with it", it connotes that she is Mekudeshes, even though she did not immerse!

Answer: The case is, she immersed beforehand for the sake of freedom. The Tevilah of freedom precedes the document, like it connotes below. It says "he immerses her for the sake of freedom, frees her, and immediately he is permitted to her."

Question: Regarding Hechsher Mikveh, it is obvious to him that we do not distinguish between a Nidah immersing for her husband or for Taharos. He said "where a Nidah immerses";

Regarding Chatzitzah, he says that Nidah [for her husband] depends on Tevilah for Tum'ah and Taharah!

Answer: Regarding Chatzitzah, there are many matters that are only mid'Rabanan, e.g. the majority [of the body is covered] and he is not particular about it, or the minority and he is particular about it;

He needs to teach that also for a Chatzitzah mid'Rabanan, we do not distinguish between [immersing] for her husband or for Taharos;

There are matters of Chatzitzah about which we say (Nidah 67a) "this is only for Taharos, but not for her husband". This refers to a Safek Chatzitzah;

Regarding a Vadai Chatzitzah, even mid'Rabanan, we are not lenient for her husband more than for Taharos.

Rashi's opinion: Rashi says that it (the distinction between Taharos and her husband) is not in the text in Nidah, due to our Sugya.

Explanation #1: This is because they (converts) are not expert in details of Mitzvos, and Yisre'elim learn from them.

Explanation #2: In Nidah (13b), Rashi explained another version, that it is because all of Yisrael are responsible for each other.

Question: In Sotah (37b), it connotes that they (Yisrael) are not responsible for converts. (It discusses 603,550 covenants on every Mitzvah, corresponding to responsibility for every Yisrael.) It does not count the Eruv Rav (converts from Mitzrayim who accompanied Bnei Yisrael)!

Explanation #3: Converts are problematic for Yisrael, because they mix with them, and the Shechinah rests only on families of proper lineage in Yisrael.

Explanation #4: It is because Yisrael are warned more about [paining] converts, and they cannot be careful to avoid paining them.