Gemara - d'Vei R. Yishmael: "Between a man and his wife, between a father and his daughter" teaches that a Na'arah Me'orasah, her father and her husband annul her vows.

Explanation: He infers that the verse discusses a Na'arah Me'orasah, for it says in the verse "bi'N'ureha Beis Aviha", and since it put "Av l'Vito" next to Ish, this implies that a father and husband annul her vows.

Explanation: [Rava] taught below (70a) that we equate [vows] before the second Kidushin to [vows] before the first Kidushin. (If an Arusah was widowed, her father can annul her vows until she remarries, just like he could annul her vows before her first Kidushin.)

Rabanan hold that we learn both of these. The verse primarily teaches about a Na'arah Me'orasah, that her father and husband annul her Nedarim. It mentions two Havayos (Kidushins - "Hayo Sihyeh") to equate the second to the first.

Question: Since Tana d'Vei R. Yishmael uses the entire verse to equate the Havayos, what is his source that an Arus can annul Kodmin?

Answer: He holds that we do not need a verse for this. Granted, the Torah excluded Kodmin regarding a Ba'al, i.e. because there is no father (she left his Reshus)...

We have this exclusion only in the case it was written, i.e. after Nisu'in, and the father is not applicable [to Hafarah]. Then, a Ba'al cannot annul Kodmin;

However, an Arus, who annuls in partnership with the father, he can annul even Kodmin, for regarding the father, there are no Kodmin. This is from the great Chacham R. Shmuel.

Gemara - Question: And Rabah, this of Tana d'Vei R. Yishmael, what does he do with it?

Explanation: I.e. the verse from which Tana d'Vei R. Yishmael expounds his Drashah, what does [Rabah] learn from it?

Explanation: Nidrei Inuy Nefesh are explicitly written - "Kol Neder v'Chol Shevu'as Isar Le'anos Nafesh!" We need "Bein Ish l'Ishto" for matters between him and her;

Below (81b), we explain what these [matters] are.

Question: According to Tana d'Vei R. Yishmael, what is his source for matters between him and her?

Answer: Perhaps he learns both of them (this, and that a father and Arus annul together) from it ("Bein Ish l'Ishto Bein Av l'Vito").

Opinion #1: Also, just like a husband can annul only his wife's vows with Inuy Nefesh and matters between him and her, also a father can annul only such vows of his daughter.

Support #1 - Citation (Sifri) Question: I know only that a husband can annul only vows between him and her, and vows with Inuy Nefesh. What is the source for a father?

Citation (cont.): You can learn from a Kal va'Chomer... [we conclude] I cannot learn from a Kal v'Chomer.

Citation (cont.) Answer: "Elu ha'Chukim... Bein Ish l'Ishto Bein Av l'Vito" - you are forced to equate the father to the husband;

Citation (cont.) Just like the husband can annul only matters between him and her, and vows with Inuy Nefesh...

Support #2 - Citation (Yerushalmi) Question: "Kol Neder v'Chol Shevu'as Isar Le'anos Nafesh Ishah Yekimenu v'Ishah Yeferenu" teaches only about Nedarim with Inuy Nefesh. What is the source for matters between him and her?

Citation (cont.) Answer: We learn from "Bein Ish l'Ishto."

Citation (cont.) Question: This teaches about a husband. What is the source for a father?

Citation (cont.) Answer: Just like a husband can annul only vows with Inuy Nefesh, and matters between him and her, also a father annuls only vows with Inuy Nefesh, and matters between him and her.

Opinion #2: This is unlike the Rambam (Hilchos Nedarim 12:1), who says that a father can annul all vows of his daughter.

Explanation: An Arus, who annuls only with partnership of the father, when he annuls his portion, does he cut?

I.e. he totally cuts off half the vow and is Mevatel it, and the rest is left as strong as initially, and it was not weakened at all?

Or, does he weaken it? We do not say that he cut off half, to be Mevatel that half, and the other half is left intact. Rather, Hafarah of an Arus weakens the entire Neder.

Assertion: The Gemara asked about an Arus, and [whatever the Halachah follows is regarding an Arus,] the same applies to a father. The Gemara mentioned one of them.

Gemara: How do we ask?

Explanation: I.e. what difference does it make?

Gemara: She vowed from two olives.

Explanation: They were two known olives, and she ate both of them.

Gemara: If you will say that that he cuts off...

Explanation: Granted, Hafarah of the Arus uprooted the Isur of one of them. The other stands intact, and he is lashed for it.

However, since we do not know which one stands in its Isur, he is not lashed until he eats both of them.

Explanation: There are no lashes, because the entire Neder was weakened, and there is a mere Isur.

Question: Why must we say that there were two olives? In Shevu'os (22a), Rav Papa taught that for Konamos, one is lashed for any amount!

Answer #1: Since there is an opinion there that holds that even for Konamos, one is lashed only for a k'Zayis, we mentioned here [two olives] to broaden the matter [and make the question relevant according to both opinions].

Answer #2: Due to Shevu'ah, we mentioned this, for Shevu'ah is included in "Neder", like we said above (8a) "he vowed a great Neder to Elokei Yisrael";

Regarding a Shevu'ah, there are no lashes for less than a Shi'ur.

Answer #3: Here, "Lokeh" means that he is stricken with [an obligation to bring] a Korban for Me'ilah;

All agree that there is no Korban for less than a Shi'ur.

Support: We find [that "Lokeh" means] like this in Bava Metzi'a (43a) "he is Lokeh (suffers, and has the lower hand) from any increase or decrease in value." This is from the Rashba.

Explanation: It taught "he died that day." This refers to when he heard and was silent. It is only if he died that day, so the husband was not yet Mekayem it, that the father can annul;

However, if he died the next day, he cannot, for the husband was Mekayem it. Since he did not annul it, he revealed his intent that he is pleased with the vow. Therefore, the father, who comes from the husband's power, cannot annul.

Distinction: However, if he heard and annulled, even if he died the next day, [the father] can annul.

Implied question: Once the husband died, his Hafarah is Batel. The father must annul the husband's share with his own share!

Answer: Even so, since he already annulled, we cannot consider it like Hakamah of the husband, even though his Hafarah is Batel;

In any case, he revealed his intent that he is not pleased with the vow. What [more] should he have done?!

Support: This is proven from the Seifa, which taught "however, if he heard and was Mekayem, or was silent and died the next day, [the father] cannot annul.

If even when he heard and annulled, when he died the next day, [the father] cannot annul, it should teach so, that when he heard and annulled and died the next day, [the father] cannot annul;

This is a bigger Chidush than when he heard and was silent!

Conclusion: Surely, since it did not teach this, this shows that if he heard and annulled, even if he died the next day, the father receives authority, and he can annul.

Explanation #1: [I saw] early Meforshim say that what was taught "the husband did not hear [before he died]" is not precise. It was taught needlessly. Also in the other clauses they say so.

Rebuttal: They did not explain correctly in my humble opinion. Therefore, I see a need to explain these clauses.

Explanation #2: It seems to me that it taught "the husband did not hear" for a Chidush. Even though these vows were not Nir'u (possible to annul) to the Arus, and he did not acquire [ability to annul] them...

This is like we say below (70b) "perhaps this is only regarding vows that were not Nir'u to the Arus";

Inference: What was not Nir'eh to the Arus, he has less power in it. One might have thought that since the father annulled, and the Arus did not acquire at all, when he died, this vow is very weak, and only a little remains;

One might have thought that Hafaras ha'Ba'al suffices for that small remnant. [The Beraisa] teaches that this is not so.

Even though this vow was greatly weakened, the husband cannot annul even the little that remains.

Just like the Reisha teaches that even though the vow was not weakened at all, i.e. when the husband heard and was silent, even so the father can annul...

Also here, it teaches that even though the vow was greatly weakened, the husband cannot annul.

Explanation: Also here in this clause, we learn a Chidush when the husband annulled and the father did not hear [before the husband died]. Even so, when the husband died, the father receives authority;

The Chidush here is that he did not hear [before the husband died]. If not, this is the first case!

Implied question: Just the contrary! The Reisha teaches a Chidush that when the husband heard and was silent, even though the vow was not weakened at all, the father received authority;

We can learn [this clause] from a Kal va'Chomer! When the vow is intact, the father can annul. When the vow was weakened, like here that the husband annulled and it was not yet Nir'eh to the father, he additionally has the husband's Hafarah. Is there any question that the father can annul?!

Strengthening of question: Further, you said in the clause "her father heard" that it teaches a Chidush, that even though the father annulled, and the husband did not yet hear, and the vow was weakened greatly, the husband cannot annul.

If there were a Chidush in such a case, that the husband cannot annul, how is this a Chidush, in the same case, that the father can annul?

Answer: Indeed, surely this is so, and do not ask. We could say one way, and we could say the other way;

We could say that since the first's Hafarah was proper, for it was not yet Nir'eh to the other, the vow was weakened greatly, and only a little remains;

One might have thought that Hafarah of the other suffices for that little [remnant]. Therefore, the Reisha teaches that even that little, the husband does not receive authority [to annul it].

Also, we could say [oppositely,] that since the first's Hafarah was proper, for he annulled and it was not Nir'eh to the other, the vow was weakened greatly, and only a little remains, we should say that that little, since it is very weak, is not proper for the father to inherit it;

This is like Beis Hillel say below in the last clause of this Beraisa, that he cannot annul, for because the vow was weakened greatly, the father cannot acquire it. Also here, we should say so. The Beraisa teaches that this is not so. Even so, the father receives authority [to annul it].

This is because granted, at the time her husband annulled, it was a proper Hafarah to weaken the vow greatly, for the father did not yet hear it, even so, when he died, it is Batel. Therefore, the father is proper to acquire it;

This is unlike the last clause. Since the father is still alive, his Hafarah is not Batel. Since the vow was weakened, according to Beis Hillel, he cannot acquire the husband's share.

Question: If so, we could say oppositely! I.e. the reason when her father heard and annulled her, and her husband did not yet hear it before her father died, that the husband does not receive authority...

This is because the vow was weakened greatly, and the husband cannot acquire it;

However, when the father did not annul, and the vow is strong, the husband acquires it!

Answer: You cannot say so. If when he did not annul, the husband can acquire it, also when [the father] did annul, it is proper that [the husband] acquires it;

We find in the other clause that even though the husband annulled, and the father did not yet hear it, the father can annul. This shows that the law of one who can annul is not worse due to weakening of the vow.

Question: Perhaps this is only for a father, who is stronger [regarding Hafarah], but the husband, I can say that due to weakening of the vow he cannot annul, but if it was not weakened at all, he can annul!

Answer: You cannot say so. If weakening is significant, also a father cannot annul [if it was weakened], for we find in the Seifa that Beis Hillel say that because the vow was weakened, the father cannot annul;

Therefore, if when one of them annulled and died, and the other did not yet hear it, the vow is weakened, [also] when the husband heard and annulled, and the father did not yet hear it, how can the father annul?!

Rhetorical question: Rather, what can we say? Since he died, the first one who annulled, his Hafarah is Batel, and due to this weakening, the other's rights are not diminished;

Automatically, we learn that when he taught that the father heard and annulled, and the husband did not hear until the father died, the husband does not receive authority.

Explanation: [The Beraisa] discussed when [the father] annulled, and [the husband] did not yet hear it for a Chidush. The same applies when the father did not annul; the husband does not receive authority.

The same applies to the clause in which the husband heard and annulled, and the father did not yet hear it until the husband died;

Suggestion: Perhaps the reason that the father receives authority is because the vow was weakened, and only a little remains!

Rejection: The Reisha already teaches that when the husband heard and was silent and died, so the vow was not weakened at all, even so, when the husband dies, the father receives authority.

Explanation: In this clause we learn a bigger Chidush than in the clause in which her father heard and annulled. Also that [clause] concludes "when the father died, the husband does not receive authority";

There we can say that granted, at the time the father annulled, it was a proper Hafarah, and the vow was weakened greatly, and only a little remains;

Since the husband did not hear it, even though when the father died, the vow is like it was initially, for when the father died, his Hafarah is Batel, and it has no effect...

Therefore, since the vow is strong, it is proper that the husband, who does not have great power, he cannot annul;

However, here that the vow was weakened, for the husband annulled, and the father did not hear it, and the vow is still weakened, for the husband's Hafarah was not Batel, for [the husband] is alive...

One might have thought that since it is weak, and only a little remains after the father's death, for that little bit, the husband's Hafarah suffices;

Even so, the husband cannot annul, even though the father never acquired [rights to annul] in this vow, for he never heard it, and it is very weak, for the husband annulled, and he is still alive...

Even so, the husband cannot annul, for it is a uniform law that a husband (Arus) annuls only in partnership.

Support: This is why it said this expression (a husband annuls only in partnership), and did not say "the husband does not receive authority", like was taught above;

This is because above, the father acquired [rights to annul], and his Hafarah was Batel. It is proper to teach "the husband does not receive authority", which implies that the father acquired, and the husband does not receive his authority;

However, here the father did not acquire at all, and we can say that the husband's Hafarah is not Batel, since he did not die. Even so, it is a uniform law that a husband annuls only in partnership.

Summary: There are four clauses in this Beraisa until here. Two discuss when the father receives authority, and two discuss that the husband does not receive authority. Each one has a Chidush, like I explained.

They are taught in their order. He receives authority, and he does not receive authority. He receives authority, and he does not receive authority. So it seems to me to explain these clauses.