Mishnah
Mishnah

Commentary for Yevamot 3:1

אַרְבָּעָה אַחִין, שְׁנַיִם מֵהֶן נְשׂוּאִים שְׁתֵּי אֲחָיוֹת, וּמֵתוּ הַנְּשׂוּאִים אֶת הָאֲחָיוֹת, הֲרֵי אֵלּוּ חוֹלְצוֹת וְלֹא מִתְיַבְּמוֹת. וְאִם קָדְמוּ וְכָנְסוּ, יוֹצִיאוּ. רַבִּי אֱלִיעֶזֶר אוֹמֵר, בֵּית שַׁמַּאי אוֹמְרִים יְקַיְּמוּ, וּבֵית הִלֵּל אוֹמְרִים יוֹצִיאוּ:

If there were four brothers, two of them married to two sisters, and they died, the surviving two perform chalitzah, but not yibum. [For since both women are linked to each brother, the first to perform yibum violates "the sister of his linked one," who is like his wife.] If they were beforehand and married them, they must send them away. R. Eliezer says in the name of Beth Shammai: They may keep them, and Beth Hillel say: They must send them away. [The gemara reverses this, viz.: Beth Shammai say: They must send them away, and Beth Hillel say: They may keep them. For in all places, Beth Shammai's is the stringent ruling, and Beth Hillel's the lenient, except for those noted instances where the opposite is the case. And in general we say: "Beth Shammai in the place of Beth Hillel is not a Mishnah." That is, wherever we find in the Mishnah that Beth Shammai's is the lenient ruling (where it is wont to be Beth Hillel's, so that Beth Shammai stands in the place of Beth Hillel), we assume it to be not a (bona fide) Mishnah, but mistaken, and we reverse it (unless it be one of the noted Mishnayoth where Beth Shammai takes the lenient view and Beth Hillel the stringent one. And in Eduyoth, it is listed in the name of R. Eliezer among the lenient rulings of Beth Shammai and the stringent ones of Beth Hillel.)]

Bartenura on Mishnah Yevamot

ארבעה אחין. חולצות ולא מיבמות – since both of them are levirate relations one to the other. The first [brother] who undergoes levirate marriage came in contact with the sister of his levirate relation and is like his wife.
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English Explanation of Mishnah Yevamot

Introduction Mishnayoth one through four are all one long mishnah dealing with a case of four brothers, whom we will call, Reuven, Shimon, Levi and Judah, two of whom married two sisters, Rachel and Leah.
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Bartenura on Mishnah Yevamot

ב"ש אומרי יקיימו ובה"א יוציאו – In the Gemara (Talmud Yevamot 28a) reverses them that the School of Shammai states that they should be put away (i.e., divorced), and the School of Hillel states that they may remain wedded, for in every place, the School of Shammai is stringent and the School of Hillel is lenient except from those known places where the School of Shammai is more lenient and the School of Hillel is more stringent (see, for example, the first five Mishnayot in Tractate Eduyot, Chapter 5, of which this text is taken), and thus we say, that generally, the School of SHammai in the place of the Schol of Hillel is not a Mishnah, meaning to say, that wherever we find in the Mishnah that the School of Shammai are lenient and the School of Hillel, where it is their manner to be lenient, but and it is found now that the School of Shammai stands in the place of the School of Hillel, it is not a Mishnah and it is a corrupted text and it is necessary to reverse it unless it is from the known Mishnayot which are from the leniencies of the School of Shammai and the stringencies of the School of Hillel. And in Tractate Eduyot (Chapter 5, Mishnah 5), in the name of Rabbi Eliezer, it enumerates the leniencies of the School of Shammai and the stringencies of the School of Hillel.
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English Explanation of Mishnah Yevamot

Four brothers: two of whom were married to two sisters, if those who were married to the sisters died, behold these must perform halitzah but may not have yibbum. If they preemptively married them, they must divorce them. Rabbi Eliezer said: Beth Shammai holds that they may retain them, and Beth Hillel holds that they must divorce them. Reuven and Shimon marry Rachel and Leah and then both die. Rachel and Leah are technically liable for yibbum or halitzah with either Levi or Judah. The mishnah teaches that neither Levi nor Judah may have yibbum with either sister, because each sister is the sister of his z’kukah (a woman with whom he is liable to have either yibbum or halitzah). In other words Leah is liable to have yibbum or halitzah with each brother as is Rachel. They are both considered to be “z’kukah” to both brothers. If Levi or Judah were to have yibbum with either one, he would be having relations with the sister of his z’kukah, which is forbidden just as it is forbidden to have relations with one’s wife’s sister. Even after one sister has had halitzah with one of the other brothers, thereby ending her status as z’kukah, the other may not have yibbum because any one woman is forbidden to him at the time when she becomes liable for yibbum, remains forbidden forever.
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English Explanation of Mishnah Yevamot

If the brothers did marry the sisters, against the ruling in clause one, they must divorce them. Although the marriage is valid and therefore requires a divorce, it is forbidden and therefore a divorce is mandatory.
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English Explanation of Mishnah Yevamot

According to Rabbi Eliezer, the previous ruling is only according to Beth Hillel. Beth Shammai disagrees and rules that the marriage may be upheld.
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