מתני׳ חמש עשרה נשים פוטרות צרותיהן וצרות צרותיהן מן החליצה ומן היבום עד סוף העולם
The Torah law obligating a man whose brother died without children [yavam] to marry his deceased brother’s widow [yevama] or to free her from her levirate bonds through the act of ḥalitza applies only when it is permitted for the widow to marry her surviving brother-in-law. However, in cases where the yevama is forbidden to her yavam due to her status as a close family relative, the mitzva of levirate marriage is not applicable, and she is exempt from both levirate marriage and ḥalitza.
The Sages further taught that the exemption of a yevama from levirate marriage also exempts her rival wife. In other words, if the deceased brother had two wives, each a so-called rival of the other, and only one wife is a relative of the surviving brother, then the rival wife is also exempt from both levirate marriage and ḥalitza. Moreover, if that same rival wife entered into levirate marriage with a different brother of the deceased, one to whom she is not forbidden, then were this third brother also to die childless, so that the obligation of levirate marriage would again be incurred by the second brother, not only is the forbidden rival wife exempt from levirate marriage and ḥalitza, her new rival wives from her second marriage are also exempt.
That is to say, any other wife of the third brother is exempt from the mitzva of levirate marriage, as she is the rival wife of that first rival wife, who was exempted from levirate marriage following her first husband’s death due the exemption of her original rival wife. The same principle applies if that second rival wife subsequently enters into levirate marriage with another permitted brother, and so on. In summary, every widow who is exempt from marrying her brother-in-law due to her status as rival wife of a forbidden relative is treated as a forbidden relative herself and is therefore exempt from both ḥalitza and levirate marriage and causes exemption for future rival wives as well.
MISHNA: The mishna describes various cases that invoke the principles above. Fifteen categories of women constitute familial relations that are forbidden as incestuous, and consequently, these women exempt their rival wives and the rival wives of their rival wives from ḥalitza and from levirate marriage forever, i.e., they also exempt rival wives of rival wives of rival wives, and so on.
ואלו הן בתו ובת בתו ובת בנו בת אשתו
And these women are: The daughter of the yavam, i.e., the deceased brother had married a daughter of his brother, which means that when he died childless, his brother’s own daughter came before her father for levirate marriage, and therefore she is exempt. And the same applies if the deceased brother’s widow is the daughter of the daughter of the yavam, or if she is the daughter of his son, or the daughter of his wife.
ובת בנה ובת בתה חמותו ואם חמותו ואם חמיו
And similarly, if the yevama is the daughter of the son of the wife of her yavam or the daughter of his wife’s daughter, or if she is the mother-in-law of her yavam, or his mother-in-law’s mother, or his father-in-law’s mother, then she is exempt from ḥalitza and levirate marriage.
אחותו מאמו ואחות אמו ואחות אשתו ואשת אחיו מאמו
The mishna continues its list of close relatives. If the yevama is the maternal half sister of the yavam, or if she is the sister of his mother, or his wife’s sister, then she is exempt from both ḥalitza and levirate marriage Or if she was the wife of his maternal half brother, and after this brother died or divorced his wife, she married another of his father’s brothers, who was not her relative, and this brother died, she is exempt. In this case, the obligation to enter into levirate marriage should be incurred by the surviving brother, but since she was previously the wife of his maternal brother, she is exempt.