Yevamos, Chapter 13, Mishnah 9. The Mishnah deals with a man who was married to two women whose marriages are not from the Torah but only rabbinic, and who died childless, so that both of them fall to yibum. We will look at three cases: two minor orphan girls, two deaf-mute women, and the combination of a minor and a deaf-mute woman, where the fundamental distinction between the two comes to light.
Two minor orphan girls:
"Mi shehayah nasui lishtei yesomos ketanos umeis, ba yavam al harishonah, vechazar uva al hasheniyah, o sheba achiv al hasheniyah - lo pasal es harishonah" - if a man was married to two minor orphan girls and died, and the yavam had relations with the first and then had relations with the second, or his brother had relations with the second, he has not disqualified the first. Both are minors below the age of mitzvos, and therefore their marriages are only rabbinic, and consequently the yibum performed with them is also only a rabbinic yibum.
The reason is that halachah views relations with a minor orphan girl as a doubt, whether they effect an acquisition or not. Once he has performed yibum with the first, then if the relationship is effective - both the yibum and the marriage of a minor orphan girl - he may keep the first, since her acquisition took effect, and the relations with the second are nothing but adultery, a forbidden relationship alone.
And if the first acquisition is no acquisition, then both of them are strangers who are not connected to this situation at all, and there is no problem of yibum with two wives of the same man, since from the outset they were never bound to the husband and there was no acquisition here. It emerges that since the matter is a doubt, if anything is going to take effect it will take effect with the first, and the second will not take effect.
"Vechein shtei chershos" - and the same applies to two deaf-mute women. Here too the betrothal is only rabbinic, and therefore the same law applies.
The difference between a minor and a deaf-mute woman:
A minor: her marriage is a doubt, meaning either it takes effect completely or it does not take effect at all.
A deaf-mute woman: as the Sages understood this relationship, the bond with her has the status of a 'partial acquisition'. To a certain degree he has betrothal with her, but it is not a complete betrothal, and there remains in her a potential that is not fully married, and that portion can be seized by another man.
He had relations first with the minor:
"Ketanah vechershes - ba yavam al haketanah vechazar uva al hachershes, o sheba achiv al hachershes - lo pasal es haketanah" - in the case of a minor and a deaf-mute woman, if the yavam had relations with the minor and then had relations with the deaf-mute woman, or his brother had relations with the deaf-mute woman, he has not disqualified the minor. This law is the same as the law of two minors. If the betrothal of the first takes hold, it takes hold completely, and it is the only marriage that counts, and consequently it is the only yibum that counts, and the one who has relations with the second can accomplish nothing. And if the minor is not married, then nothing happened here at all, and the deaf-mute woman is able to be the yevamah. Either way, the deaf-mute woman does not disqualify the minor: if it takes hold, it takes hold, and if it does not take hold, she is like an unrelated woman with whom he had relations or a marriage.
He had relations first with the deaf-mute woman:
"Ba yavam al hachershes vechazar uva al haketanah, o sheba achiv al haketanah - pasal es hachershes" - if the yavam had relations with the deaf-mute woman and then had relations with the minor, or his brother had relations with the minor, he has disqualified the deaf-mute woman. Since the acquisition of a deaf-mute woman is a partial acquisition, a certain marriage potential remains in her, and there is no complete acquisition of marriage here. Therefore, when he himself or his brother has relations with the minor, those relations seize everything that remains.
The minor is able to disqualify the bond with the deaf-mute woman, because something remains in her that the yibum can seize and acquire. It emerges that here there are two rival wives who both have a bond of yibum, whether with the same man or with two yevamim, and that is a problem, and therefore the bond he had with the deaf-mute woman is disqualified.
In summary: in the marriage of a minor the acquisition is a doubt - either it takes effect completely or it does not take effect at all, and therefore relations with the second accomplish nothing. In the marriage of a deaf-mute woman the acquisition is partial, and a portion remains in her that another man's relations can seize. Hence: one who has relations first with the minor has not disqualified the minor; whereas one who has relations first with the deaf-mute woman and afterward with the minor has disqualified the deaf-mute woman.