Explanation #1 (Rashi): Inheritance does not apply to Nochrim after they converted.

Observation: In Kidushin (17b) it connotes that they do inherit! We say in Kidushin that mid'Oraisa, a Nochri inherits his father!

Note: Most explain that this is not a proper challenge, just a connotation that we discuss before conversion. Mishmaros Kehunah - Tosfos understands Rashi to say that they do not have inheritance even after conversion. It is a proper challenge.

Explanation #2: Rather, it says here "inheritance does not apply to them", i.e. the law of Bechorah.

Citation: In Yevamos (62a) it says in a different version "also initially, Peru u'Rvu applies to them."

Explanation: It does not mean that they are obligated, for in Sanhedrin (59b) it is proven that [a Nochri] is not commanded Peru u'Rvu. Rather, it means that his descendants trace their lineage through him. This is "he fulfilled Sheves" that we say here;

And regarding a slave, it says in Yevamos (62a) that all agree that he did not fulfill [Peru u'Rvu], for he does not have lineage.

Explanation: The one who says that Mezahamin, for we cast him after the Nochri, like Rashi explained;

This is called Mezahamin, for Nochrim are Mezuhamin, like we say in Shabbos (146a) "at the time that the snake had Bi'ah with Chavah, it cast filth in her", and this did not cease from Nochrim.

Explanation #1: The one who says that if a Nochri or slave had Bi'ah with a Bas Yisrael, the child is Kosher, for we attribute him to the Nochri [to whom Mamzerus does not apply];

However, the one who says that the child is a Mamzer, we attribute him to the Bas Yisrael, and therefore Mamzerus applies.

Explanation #2: Rashi explained oppositely.

Proof (for Explanation #1): In Yevamos (17a, it says that Sancheriv exiled the 10 tribes and settled them) "ba'Chlach uv'Chavor...", and R. Yochanan said that [the lineage of] all these places is Pasul;

[Rav Yehudah said] when I said this in front of Shmuel, he said "Ki Yasir Es Bincha me'Acharai" - your son that comes from a Bas Yisrael is called your son, but your son who comes from a Nochris is not called your son, rather her son;

Explanation: They are not disqualified, because the lineage follows the Nochris. (The children are Nochrim. They may marry Yisraelim, i.e. after conversion. We are not concerned for descendants of females of the 10 Shevatim, lest they are Mamzerim, for we have a tradition that) Bnos Yisrael of that generation became sterile.

Support: Also it is proven in Yevamos there that calling him "your son" causes that he is a Mamzer.

Pesak: We rule like him in Chulin (132a), and we rely on this nowadays for the son of a Leviyah or Kohenes married to a Yisrael, to exempt him from five Sela'im (Pidyon ha'Ben).

Explanation: We do not give a share to a woman at the granary, like it says in Yevamos (99b, lest she continue taking after she is divorced, or lest she be secluded with a man).

Explanation: Even Kedushas Leviyah is uprooted from [a Bas Kohen], and she is worse than a Leviyah married to a Kohen who was captured [by Nochrim, and we assume that they had Bi'ah with her]. Even though [the latter] is disqualified from Terumah, her Kedushah is not uprooted for five Sela'im (e.g. if she will later marry a Yisrael);

However, a Kohenes, whose Kedushah comes from her body, when she is profaned, her Kedushah is totally uprooted.

Explanation: Rather, the son must redeem himself, even though the father had no obligation.

Support: The same applies in our Mishnah (46a). If she was pregnant when she converted or was freed... [the son must redeem himself, even though his father was exempt].

Question: In Kidushin (29a), regarding Mitzvos that a father must do to his son, we expound "Tipadeh Tifdeh" - a woman, whom others are not commanded to redeem her, is not commanded to redeem herself;

Likewise, this son, whom others are not commanded to redeem him, should not be obligated to redeem himself!

Answer: This son is unlike a woman. Pidyon does not apply to [a woman] at all, for any father;

However, here, if his father was a Yisrael, he would be obligated to redeem [this son].

Explanation #1: Rashi's Perush connotes that he learns from the expression of Leidah (birth).

Question: In Nidah (40a) it explains that his mother does not observe days of Tum'ah and days of Taharah [of a Yoledes] for [a Yotzei Dofen], for it says "Ishah Ki Sazri'a v'Yaldah Zachar" - this is only if she gave birth from the place where she is Mazri'ah (gives off her seed). It does not expound from the expression of Leidah!

Explanation #2: Rather, here we learn from a Gezeirah Shavah "Leidah-Leidah" from there. R. Shimon here teaches like he taught elsewhere, like it says below, that he includes there a Yotzei Dofen from "Teled", that she observes days of Tum'ah and days of Taharah.

Question: There it says that R. Shimon agrees about Kodshim that [a Yotzei Dofen] is not Kadosh, for he learns from Bechor, about which it is written Peter Rechem...

And it asks that he should learn "Leidah-Leidah" from man, for which we include Yotzei Dofen from Teled, for [these are more similar, for they apply to even to] a Pashut (non-Bechor), [they are not automatically] Kodesh, [they are not limited to] a male, and [they are not] Matanos (given to Kohanim);

It answers that there are more similarities to a Bechor - [the verses teaching about them mention] "Imo," they are animals, they are Kodshim, and Pigul, Nosar and Tamei apply to them.

Summation of question: Also here we should learn from Bechor Behemah, for [also] it is a Bechor, they are males, and they are Matanos [Kehunah]!

Answer: The other similarities are greater - man from man, and they are not Kadosh, and Pigul, Nosar and Tamei do not apply to them.

Bechor Adam for Kehunah, about which it is written Peter Rechem, R. Shimon cannot learn from Bechor of inheritance, for regarding Bechor Adam of Peter Rechem it is not written Leidah.

Question: Since we expound the verse for Bechor, if so, in Bava Basra (127a) that we expound that a Tumtum who was torn and found to be male, that he does not decrease the Bechor's [extra] portion, for it says "v'Yaldu Lo Banim" - he must be a [known] son from the time of birth;

And this that he does not receive a double portion it expounds from "v'Hayah ha'Bechor" - he must be a son from the time of birth;

And similarly there (142b) we expound that a son born after his father's death does not decrease the Bechor's portion, for it says "v'Yaldu Lo", and this that he does not receive a double portion it expounds from "Yakir";

Summation of question: What is the reason? We should learn everything from "v'Yaldu Lo", since we establish it to discuss a Bechor!

Answer: If there were not two verses, we would establish "v'Yaldu Lo" to teach only that he does not receive a double portion, for it is more reasonable to establish it for a Bechor that he does not receive the Bechor's [extra] portion, than to establish it for a Pashut, that he does not decrease the Bechor's portion.

Support: There are not two verses for Yotzei Dofen, and we expound that he does not receive a double portion, and we do not expound it to teach that he does not decrease.

Question: For this reason itself, a Yotzei Dofen should be a Bechor for five Sela'im, even though it is written "Peter Rechem", like we find above (19a) that a Yotzei Dofen and the one [born] after it, R. Tarfon says that both of them graze until they get Mumim;

The Gemara explains that he is unsure whether or not a Bechor in one respect is a Bechor, even though also there it is written "Peter Rechem"! (Since R. Shimon is sure that a partial Bechor is a Bechor, he should hold that the first is the Bechor!)

Answer: R. Shimon's reasoning is unlike R. Tarfon's. Even though it is more obvious to [R. Shimon] that the one [born] after [a Yotzei Dofen] is a Bechor than to R. Tarfon, even so he holds that a Yotzei Dofen is worse, and he excludes it from Peter Rechem.