A Beraisa was found that says 'both of these [laws in the Mishnah] are a stringency of Shevu'os over Nedarim.'

Explanation #1: Shigegas Shevu'os are forbidden, and Shigegas Nedarim are permitted. (We said above that likewise Shevu'os Havai are forbidden, and Nidrei Havai are permitted.)

Rebuttal (and Explanation #2): [The Beraisa] was not said about this, rather, about [the following];

(Mishnah): 'I swear that I will not eat this loaf, I swear that I will not eat it [... and he ate it], he is liable only once. This is a matter forbidden in Nedarim, and permitted in Shevu'os.

And a matter permitted in Nedarim and forbidden in Shevuos - the same applies to matters of himself and matters of others [both to intangible matters and tangible matters; Nedarim do not apply, but Shevu'os apply].

Limitation (R. Ba citing Shmuel): If one swore that Ploni gave a Maneh to Almoni, and it turns out that he did not give, since it is not b'Yado for the future (to make Ploni give, so he is exempt for a Shevu'ah that he will give), also in the past it is not b'Yado. (This shows that Shevuos do not apply in all cases to matters of others. We explained this like MEICHAL HA'MAYIM.)

Question (Reish Lakish, to R. Ba): What did R. Akiva come to add to Beis Hillel's words? It was taught there [if one was Pose'ach with Shabbos and Yom Tov, for he overlooked that his vow will include these days, at first, Chachamim said that those days are permitted and other days are forbidden]. R. Akiva came and taught that a vow that was partially permitted is totally permitted. (Beis Hillel already taught so in our Mishnah!)

Answer #1 (R. Ba): There, a Neder that needs a Chacham to permit it, you say that a vow that was partially permitted is totally permitted. Here that it does not need a Chacham to permit it, all the more so! (However, you could not learn from here to there, where it needs Heter Chacham.)

Answer #2 (R. Yosi citing R. Heila): Beis Hillel permit here due to a mistaken Neder (not because it was partially permitted). Had I know that my father and brother were there, I would not have vowed.