Nedarim Chapter 9, Mishnah 7. This mishnah is a direct continuation of the previous one, in which Rabbi Akiva presented the rule that "a vow that was partially released is entirely released" - that is, once part of a vow has been permitted, the entire vow becomes permitted. Our mishnah opens with the word "keitzad" (how so), meaning: give us another illustration of this rule, beyond the case brought in the previous mishnah.
"Konam she'eini neheneh l'chulchem":
A person vows that he will derive no benefit from any single member of an entire group of people. In such a case the mishnah rules: "hutar echad meihen - hutru kulan" - once one of them has been released, the vow is released with respect to all of them. When a way is found to release the vow regarding one member of the group, the vow is nullified regarding everyone.
How might such a release come about? For example, it emerges that one of the members of the group is his own father, and that was certainly not what the one making the vow intended; or alternatively, an opening or an expression of regret is found with respect to one of them, and the vow is released before a sage or before a beis din. From the moment that one individual has been released, all of them are released.
Vows that are dependent on one another:
All of this applies when everything was included in a single vow: "that I derive no benefit from all of you." But what is the law when we are dealing with separate vows, where he says "she'eini neheneh la'zeh v'la'zeh" - that I derive no benefit from this one and from this one? The Gemara explains that by the phrase "to this one and to this one" he means that each later person should be forbidden exactly like the first: he forbade Reuven, and like him he asked that Shimon be forbidden, and like him Levi, and like him Yehudah, and so on. It turns out that the vows are dependent on one another.
From here there are three situations:
"Hutar harishon - hutru kulan": once the vow has been released with respect to the first person about whom he vowed, all of them become permitted, since they all trace back and rely upon him. The one making the vow began by forbidding Reuven, and afterward said that Shimon is like him and Levi is like him, and since everything traces back to Reuven, when Reuven's vow is released all of them are released.
"Hutar ha'acharon - ha'acharon mutar v'chulan asurin": if he released only the last vow, that one alone is permitted and all the rest remain forbidden.
If the middle one was released: "heimenu ul'matah - mutar, heimenu ul'ma'alah - asur." The vows that came after it are permitted, while those that preceded it remain forbidden, since the later ones depend on the earlier ones and not the earlier ones on the later.
"She'eini neheneh la'zeh korban v'la'zeh korban":
The law is different when the one making the vow attaches the term "korban" to each and every person. As we learned at the beginning of the tractate, the standard of every vow is that the item is rendered forbidden like a korban; and once he has stated regarding each person separately that benefit from him is forbidden like a korban, each one is an independent vow standing on its own, not dependent on the others.
Therefore the mishnah rules: "tzerichin pesach l'chol echad v'echad" - one who wishes to release them all must find an opening for each and every vow separately, since these are entirely separate vows.
In summary: in this mishnah we learned how the rule "a vow that was partially released is entirely released" is applied. Where he says "konam that I derive no benefit from all of you" - once one is released, all are released. Where he says "that I derive no benefit from this one and from this one," so that the vows are dependent on one another - if the first is released, all are released; if the last is released, only the last is permitted; and if a middle one is released, from it and downward is permitted and from it and upward is forbidden. But where he says "korban to this one and korban to this one," so that each is a vow in its own right - an opening is required for each and every one.