Yevamot, Chapter One, Mishnah Two
This mishnah is a continuation of the previous and it explains many of the details.
I) How do they exempt their rival wives?
A) If his daughter or any other of these forbidden relatives was married to his brother who also had another wife, and he died, then just as his daughter is exempt so is her rival exempt.
B) If his daughters rival went and married a second brother of his, who also had another wife, and he died, then just as the rival of his daughter is exempt so is his daughters rivals rival exempt, even if there were a hundred [brothers].
II) How is it that if they had died, their rivals are permitted?
A) If a mans daughter or any other of these forbidden relatives was married to his brother who also had another wife, and his daughter died or was divorced, and afterwards his brother died, her rival is permitted.
B) The rival of any one who can make a declaration of refusal but did not make a declaration of refusal, must perform halitzah and may not have yibbum.
Section one: This section explains the opening statement of mishnah one, Fifteen [categories of] women exempt their rival wives and the rival wives of their rival wives and so on ad infinitum from halitzah and from yibbum. For the sake of clarity, I will explain it again here. Reuven and Shimon are brothers. Shimon marries Reuvens daughter. When Shimon dies without children, Reuven cannot perform yibbum with his own daughter. Hence, she and all of her rival wives are not liable for yibbum. If Reuven and Shimon had a third brother, Levi, and Reuvens daughters rival wife married Levi and then Levi died without children, the rival wife is not liable for yibbum with Reuven and neither are any of Levis other wives. This law is true even if there are 100 brothers.
As an aside, this mishnah also teaches that if there was a third brother, for whom none of the dead brothers wives was prohibited, they are liable to have yibbum or halitzah with him. The exemptions are only in a case where Reuven was the only brother.
Section two: This section explains the second section of mishnah one, If any of them died, or made a declaration of refusal, or were divorced, or were found incapable of procreation, their rivals are permitted. If Reuvens daughter died or was divorced before Shimon, her husband, dies, her rival wives are permitted to have yibbum with Reuven.
There is a special rule regarding the wife who could have made a declaration of refusal (meun) but did not. As we recall, this wifes marriage, arranged by her brother or mother, is of only rabbinical status (and not biblical). Her liability to have yibbum is therefore only rabbinic and not biblical. If she were to refuse the marriage, the rival wives are certainly liable for yibbum. However, even if she does not, her rival wives are not totally exempt. They are rabbinically exempt, because the rival wife cannot have yibbum with the yavam, but they are biblically liable, because the rival wife was not biblically married to the brother. The solution in such a case is for the yavam to perform halitzah. As we shall see throughout the tractate, in cases of doubt whether or not yibbum should or can be performed, the solution is usually the performance of halitzah, which avoids the possibility of forbidden sexual relations.