The Mishnah (3:1) discusses the case of four brothers, two of which were married to two sisters. Those two brothers died leaving the two sisters as widows. The Mishnah teaches that the surviving brothers must perform chalitzah and they cannot perform yibum. The Bartenura explains that since the sisters are zekukim -- require yibum or chalitzah -- each is defined as the achot zekukaot. In other words, one cannot before yibum to one of the sisters since she is considered the sister of the other woman with which there is a zika. The zika makes here considered "like" his wife. Consequently, it is similar to a yavama that has an issur arayot -- a forbidden relationship.
The Tosfot Yom Tov comments that do not think that if chalitza is performed to one, thereby severing the zika, that he can performed yibum to the other. The reason is that since at the time of nefila, at the time the brother died, she was assur to him, she continues to be assur to him. Recall that last week we explained that normally one is not allow to marry a woman that was married to his brother. It is only in the context of yibum that she is permitted to him. We can understand that since at the time when the obligation of yibum would have been generated she is assur, the basic prohibition of marrying one's brother's wife remains in place. Nevertheless, since the zika, this bond, is rabbinic, chalitzah is still required.
The Gemara attempts to prove from this Mishnah the law of zika. The Gemara however counters that there might be a different reason. Perhaps the law of zika does not exist and the reason why the brother cannot both perform yibum is out of concern that if one performed yibum and then the other died before performing yibum, the other yavama will then be exempt from yibum or chalitzah (since she is now his wife's sister). In other words, by performing yibum to one, he effectively was mevatel (cancelled) the mitzvah of yibum. It is out of this concern that both brothers must perform chalitzah instead.
Questions can be asked on both understandings of the Mishnah. According to the understanding that it is not based on zika, one could perform chalitzah first and then one would be able to perform yibum. Why must both brothers perform chalitzah? The Ritva however explains that there is a concern that the order might be reversed and yibum performed first, which would then remove the possibility of performing chalitzah to the other yavama as explained above.
Even according to the understanding based on zika, one could ask that one should be able to perform chalitza to the yavama whose husband died second, and then perform yibum to the first wife. That is because the first yavama was initially permitted for yibum when her husband died. It was only after, when the second husband died that this issue of achot zekukato came into play. The Rashba (28b, s.v. ha de'akshinai) explains that even according to that understanding based on zika, there is a concern the one might get the order wrong and perform yibum first, and mevatel the mitzvah.
The Tosfot Yeshanim however explains that if there is a law of zika, it would be severe, and no one would make that mistake and have a relationship with an achot zekukato -- tantamount to rabbinic arayot. Instead, he explains, once the first wife beomes assur even momentarily, that issur continues.
We however rule that also long as she was permitted at the time the husband died, then even if there was a period that she was assur he would be able to perform yibum. The Tosfot however explain that there is a concern that a different mistake will be made, if we allow chalitzah followed by yibum. One will certainly perform chalitzah first, but it might be performed with the first yevama instead. If that were the case, since the second yevama was assur to him from the time her husband died, she will still be assur and one subsequently performing yibum would be a prohibitted. (See also Kesef Mishnah Yibum 6:4).
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