Before us is Mishnah 6 in the second chapter of Maseches Yevamos, which deals with a man who betrothed one of two sisters and does not know which of them he betrothed, and with the implications of this doubt for the laws of divorce, chalitzah and yibum.
"Mi shekiddesh achas mishtei achayos v'eino yode'a ei zu mehen kiddesh" - one who betrothed one of two sisters and does not know which of them he betrothed:
A man performed an act of betrothal with one of two sisters, and he does not know with which of them he did so. The result is that he does not know which one is his wife and which one is his wife's sister. Therefore the Mishnah rules: "Nosen get lazo v'get lazo" - he cannot maintain a marriage with either of them, since it is possible that precisely this one is his wife's sister, who is forbidden to him, and so he must give a get to both of them.
"Mes, v'lo ach echad - choletz lishtayhen" - if he died and he had one brother, that brother performs chalitzah with both of them:
If the man who betrothed her died and left only one brother, that brother faces two possible yevamos, and he does not know which of them is his brother's widow. He must perform chalitzah with both of them, since each of them is possibly bound to him for yibum, and without chalitzah she would not be permitted to marry anyone else.
Three other options are closed to him:
Yibum with one of them: He may not perform yibum, lest the woman before him is the sister of the one bound to him. As was explained earlier, the sister of the woman bound to him is treated somewhat like his wife's sister and is forbidden to him, though this is not a full Torah prohibition but a rabbinic one.
Chalitzah with one and yibum with the second: This too may not be done, since perhaps the one with whom he performed chalitzah is his true yevamah, and the second one then turns out to be the sister of his chalutzah. And the sister of a chalutzah is forbidden by rabbinic law, because she resembles the sister of his divorcee, who is forbidden to him because she was his wife's sister.
Yibum first: Certainly he may not begin with yibum, for if the second woman, the one he did not take, is the true yevamah, it turns out that he performed yibum with the sister of the woman bound to him.
From all of this it emerges that his only option is to perform chalitzah with both of them.
"Hayu lo shnayim - echad choletz v'echad meyabem" - if he had two brothers, one performs chalitzah and one performs yibum:
If the deceased left two brothers, one of them first performs chalitzah with one of the sisters, and the second performs yibum with the other. Both possible scenarios work out well:
If the one with whom he performed yibum is indeed his yevamah, then he performed yibum properly.
If in fact the second one is the yevamah, she has already received chalitzah from the first brother and the bond has been removed; consequently the one with whom he performed yibum is no longer the sister of a woman bound to him.
"Kadmu v'chansu - ein motzi'in miyadam" - if they went ahead and married them, we do not take them away from them:
And what is the law if the two brothers did not follow this order, but instead went ahead and both performed yibum, one with one sister and one with the other? Each of them faces the doubt that perhaps the one he married is the sister of the woman bound to him. Even so, we do not take them away from them, and they are permitted to remain married to them.
The reason is this: at this point the bond has been removed one way or the other, for one of them certainly performed yibum with the correct yevamah, and consequently the other woman is no longer the sister of a woman bound to him. True, it would not have been proper to act this way from the outset, but once the act has been done and the bond has been removed, they are permitted to remain in their marriages, especially since each of the women was only possibly the sister of a woman bound to him, for from the other perspective she could have been the yevamah herself.
In summary: In this Mishnah we learned that one who betroths one of two sisters and does not know which one he betrothed gives a get to both of them. If he died and had one brother, that brother performs chalitzah with both of them and cannot perform yibum at all, neither at the outset nor after chalitzah, because of the prohibition of the sister of the woman bound to him and the prohibition of the sister of his chalutzah. If he had two brothers, one performs chalitzah and one performs yibum, and this order resolves both possibilities. And if both went ahead and married them, we do not take them away from them, since the bond has already been removed, and every prohibition they faced was only a matter of doubt.