Reference: This is explained in Gitin 40b.

Explanation: He was unsure whether or not Dina d'Malchusa Dina (the king's law is binding).

Even though [without Dina d'Malchusa Dina] he does not acquire the slave himself, here he acquires (due to Dina d'Malchusa). Or perhaps also now he acquires only his earnings!

We discuss while they are Nochrim, if they come to convert.

Explanation (R. Tam): All agree that if it is [properly] eaten raw, Bishul Akum does not apply.

Proof: It says in Avodah Zarah (38a) that they (the two versions) argue about small fish, mushrooms, and porridge. These do not come on a king's table, but they are not eaten raw;

The Gemara did not mention things that are eaten raw, and come on a king's table, such as fruits, cheese and similar matters [for all agree that they are permitted].

Question: Why does R. Yochanan forbid an egg? It is proper to swallow it raw!

Answer: This is not an important eating.

Support: Similarly, one may move [raw] salted meat on Shabbos, for it is proper to eat it, and even so Bishul Akum applies to salted meat.

Question: (If Edim Zomemim (witnesses who testified about something they were not present to see) testified that Ploni is worthy of lashes, they are lashed like they plotted to lash him.) According to R. Akiva, what is the source that we do not divide lashes (rather, each gets the full amount that Ploni would have received)?

In Makos 5a, we learn from execution [that we do not divide]. This is learning what is possible [to divide] from impossible!

Suggestion: There, since there is a Gezeirah Shavah (between execution and lashes), R. Akiva agrees that we learn what is possible from impossible, because we do not learn a Gezeirah Shavah only partially. (Rather, we equate the two matters in every way);

However, here (Pesach) we learn from a Binyan Av (precedent, so we do not learn possible from impossible).

Rejection: Also here there is a Hekesh, like we conclude in Menachos (82b). R. Eliezer expounds from "v'Avadta" that all Avodos [of Nisan, both in the days of Moshe and for all generations] are the same;

R. Akiva did not accept this, even though also a Hekesh is not half-way!

Question: Why does R. Yehoshua [teach in the Beraisa] what he agrees [with R. Eliezer about]? He should rather teach the law about which they argue!

R. Yehoshua taught about Tevilah [alone], which R. Eliezer agrees to. He did not mention what he argues about!

[Shmuel] asks like this Shevu'os (38a).

Answer: There, [Shmuel] was meticulous about this only because the first Tana mentioned everything;

Here, it was proper for R. Yehoshua to discuss Tevilah without Milah, since R. Eliezer did not speak about this.

Question: Below (71a), R. Akiva excludes a convert who circumcised and did not immerse from [eating] Pesach, for it says Toshav v'Sachir. Like whom does R. Akiva hold?

If he holds like R. Yehoshua, why does he need a verse? Obviously he may not eat Pesach, for he is a full Nochri!

If he holds like R. Eliezer, since he is a full convert, it is unreasonable to exclude him from Pesach, like the Gemara connotes there!

Answer: Really, he holds like R. Yehoshua, but not for his reason. R. Yehoshua holds that our ancestors also immersed [and we learn from them];

R. Akiva holds that since the Torah excluded him from Pesach, we infer that he is not a convert until he circumcises and immerses.

Explanation (R. Tam): [There is no Haza'ah] without Tevilah beforehand in order to receive Haza'ah, like it says in Kerisus (9a) "just like our ancestors entered the Bris only through Milah, Tevilah and Haza'ah of blood";

That Tevilah was Kosher even at night, like it says in Parah (12:11) "he himself may immerse at night and sprinkle during the day."

Distinction: Regarding Tum'ah, there is another Tevilah after Haza'ah in order to become Tahor from Tum'ah. The Torah first says "v'Hizah", and afterwards "v'Rachatz ba'Mayim."

Explanation #1: That Tevilah is Kosher only during the day, like the Mishnah teaches in Megilah (20a) "we immerse and sprinkle only during the day."

Explanation #2: The Mishnah discusses immersing the Ezov (hyssop). We immerse the Ezov [in the Mei Chatas] only during the day;

Source: It says at the end of Maseches Parah, that if he immersed the Ezov at night, even if he sprinkled during the day, it is Pasul.

Support: This explains why the Mishnah teaches Tevilah before Haza'ah.

Implied question: The Gemara says there that we sprinkle only during the day, for it says "v'Hizah ha'Tahor Al ha'Tamei ba'Yom ha'Shelishi..." and a Hekesh equates Tevilah to Haza'ah! (A Hekesh is within one verse. The Tevilah in that verse is of the person!)

Answer: [The Hekesh to Tevilah] is in the previous verse "v'Lakach Ezov v'Taval ba'Mayim Ish Tahor v'Hizah Al ha'Ohel..." (The Gemara cited "v'Hizah... ba'Yom ha'Shelishi" only to prove that Haza'ah is during the day. The Hekesh is not in this verse.)

Support: The Yerushalmi in Megilah says "v'Taval... v'Hizah" - just like Haza'ah is during the day, also Tevilah is during the day.

Question: Since we need Haza'ah [of blood of Kodshim], how do we accept converts nowadays?

Answer: In Kerisus (9a), we learn from a verse that this is not essential.

Implied question: (Why is this difficult?) He holds that there is no Haza'ah without Tevilah!

Answer #1: Perhaps the Haza'ah did not apply to women.

Answer #2: We need this reason (the source that the women immersed) according to R. Eliezer;

We conclude that also he holds that Tevilah alone suffices, like it says above "if he immersed but did not circumcise, all agree [that he is a convert]." R. Eliezer does not hold that there is no Haza'ah without Tevilah! (Tosfos ha'Rosh - the Gemara asked according to R. Yehoshua, for he explicitly said that Tevilah without Milah is a valid conversion.)

Question: The Gemara asks that this is obvious. How does it know that Milah alone suffices?

Perhaps he holds like R. Yehoshua, that Tevilah without Milah helps, but Milah without Tevilah does not help!

Implied question: Regarding Tum'ah, one may immerse on Shabbos, because it looks like [he enters the water] in order to cool off!

Answer: Here is different, for we require two Chachamim to stand there at the time of Tevilah to inform him of the Mitzvos, like we say below (47b).

Opinion #1 (Bahag): If one who is already circumcised converts, we must extract [from the place of Milah] a drop of Dam Bris. If a baby was born circumcised, we need not extract a drop.

Explanation: Because a baby never had Orlah (foreskin), he does not need Hatafas Dam Bris. The Nochri had Orlah, and his circumcision was invalid, therefore he needs Hatafas Dam Bris.

Distinction: However, if the entire Ever was cut off, and he comes to convert, it seems that Milah is not Me'akev conversion. R. Yosi agrees that in such a case, Tevilah alone suffices.

Opinion #2: In Shabbos, R. Chananel ruled oppositely from Bahag.

Support: In Shabbos (135a), it says that Beis Shamai and Beis Hillel do not argue about one who was born circumcised. All require Hatafas Dam Bris;

They argue about one who converts when he is already circumcised.

Defense (of Bahag): It seems that Bahag rules like the Amora'im there who do not require Hatafas Dam Bris for a baby. Regarding a convert, they hold like R. Yosi in our Sugya. It connotes that the Halachah follows him.

Below (72a), R. Elazar b'Rebbi Shimon and Rabanan argue about one who converted when he was circumcised, if he is circumcised during the day or even at night;

However, all agree that he needs Hatafas Dam Bris.

Question: Perhaps there just happened to be three there! (What is the source that we require three?)

Answer: We learn from Rav Safra. They mentioned R. Chiya for he was primary in the episode (it was in his house, and he told the convert to return tomorrow) and the greatest [of the three Chachamim]. Rav Yosef mentioned R. Oshaya, the colleague of R. Chiya;

However, why did Rav Safra mention R. Oshaya b'Ribi Chiya [if not because we require three]?!

Suggestion: We can infer from here that Tevilah alone does not suffice!

Rejection: No, the Gemara teaches that circumcision without Tevilah does not help.

Explanation: This is because it says "Mishpat". Even though he already circumcised, it is considered the beginning of judgment [which must be during the day].

Explanation #1: This refers to "u'Shfatetem Tzedek Bein Ish u'Vein Gero."

Explanation #2: It refers to "u'Mishpat Echad Yihyeh Lachem vela'Ger."

Implied question: According to the opinion that mid'Oraisa, one judge suffices [what is the source to require three for conversion]?