Yevamos, Chapter Ten, Mishnah 5. This Mishnah too deals with a man who was told that his wife had died and then married her sister. Here, however, we are dealing with a whole chain of sisters: five women whom he married one after another, each of them a sister of the one before her, whether through the father or through the mother.
The chain of marriages:
"Amru lo meisah ishtecha v'nasa achosah me'aviha" - they told him that his first wife had died, and he married her sister from the father only (they do not share a mother). This is the second woman.
"Meisah v'nasa achosah me'imah" - they told him that the second had died, and he married her sister from the mother. This is the third woman, and she is not related to the first at all, only to the second.
"Meisah v'nasa achosah me'aviha" - they told him that the third had died, and he married her sister from the father. This is the fourth woman, and she is not related to the first or to the second.
"Meisah v'nasa achosah me'imah" - they told him that the fourth had died, and he married her sister from the mother. This is the fifth woman, and she is not related to the first, the second, or the third.
"V'nimtze'u kulan kayamos":
In the end it turned out that all the women were alive, and not one of them had died. Now we must clarify which betrothals took effect and which are void.
He is permitted to the first, the third, and the fifth:
The first - she was his wife from the outset, and her marriage stands in full force.
The third - the betrothal of the second never took effect at all, since her sister, the first, was alive and the condition was not fulfilled, so it turns out that he was never married to the second. And since the third and the first are not related to one another, his marriage to her is valid.
The fifth - the third and the fourth share a father, and since the third is his valid wife, the betrothal of the fourth did not take effect. And the fifth, who is related only to the fourth, is validly married to him.
"U'fotros tzaroseihen" - these three, the first, the third, and the fifth, are all fully his wives. Therefore, if he dies, yibum or chalitzah with one of them exempts her co-wives, and they are permitted to marry anyone without yibum and without chalitzah.
"V'asur ba'sheniyah u'va'revi'is":
The second and the fourth were each the sister of a wife who was alive at the time of the betrothal, and therefore the betrothal did not take effect in them at all and he is forbidden to them. "V'ein bi'as achas mehen poteres tzarasah" - they carry no exemption for their co-wives, and since they are not his wives, even if he dies they do not require yibum and are not part of the laws of yibum at all.
"U'va al ha'sheniyah l'achar misas ha'rishonah":
Now suppose the first really did die, and after her death he lived with the second for the sake of marriage. She is now permitted to him and becomes his valid wife, and from here the entire order changes.
"Mutar ba'sheniyah u'va'revi'is u'fotros tzaroseihen" - the second is his valid wife, and consequently the betrothal of the third, who is her sister, did not take effect, and the fourth is valid. Both of them are fully his wives, and if he dies, yibum or chalitzah with one exempts the other.
"V'asur ba'shelishis u'va'chamishis" - the third is the sister of the second, who is alive, and the fifth is the sister of the fourth, who is alive, and therefore the betrothal did not take effect in them. "V'ein bi'as achas mehen poteres tzarasah" - they are not his wives, and they are not part of the laws of yibum at all.
In summary: this Mishnah teaches that in a chain of sisters the marriages depend on one another: every woman whose betrothal took effect nullifies the betrothal of the sister who follows her, and the one after that takes effect once again. Therefore, when he did not live with the second, he is permitted to the first, the third, and the fifth, and they exempt their co-wives; and when he did live with the second after the death of the first, he is permitted to the second and the fourth, and they exempt their co-wives, while the others are not his wives at all and are not included in yibum and chalitzah.