Kiddushin, Chapter Three, Mishnah One
The first section deals with a person who sends an agent out to betroth a woman on his behalf and then the agent betroths the woman to himself.
The second section deals with a man who betroths a woman but sets the betrothal date to occur in thirty days. The question is, if someone else betroths her within those thirty days, is she betrothed to the first man or to the second?
1) If he says to his fellow, Go out and betroth me such-and-such a woman, and he goes and betroths her to himself, she is betrothed.
2) Similarly, if he says to a woman, Be betrothed to me after thirty days, and another comes and betroths her within the thirty days, she is betrothed to the second, [and in such cases] an Israelites daughter [betrothed] to a priest may eat terumah.
3) [But if he says, Be betrothed to me] from now and after thirty days, and another comes and betroths her within the thirty days, she is betrothed and not betrothed [to both]: [and in such cases] an Israelites daughter [betrothed] to a priest, or a priests daughter [betrothed] to an Israelite, may not eat terumah.
Section one: Reuven sends Shimon out to betroth Rachel on his behalf. Upon seeing Rachel, Shimon decides that he himself wants to betroth her, and when he proposes betrothal, Rachel agrees. She is now betrothed to Shimon and the fact that Shimon was supposed to act as Reuvens agent is irrelevant. Of course, we can be sure that Reuven will not be happy with Shimon and Shimon has acted shamefully with his friend (sounds like a movie plot). Nevertheless, this fact is not of legal significance.
Section two: The connection between this section and the previous one is that in both the woman under discussion is betrothed to the second man. In this case, Reuven betroths the woman but sets the betrothal to begin in thirty days. When Shimon betroths her within thirty days, she is betrothed to Shimon, because Reuvens betrothal has not yet begun. When the thirty days are up, Reuvens betrothal does not kick-in, because she is already fully betrothed to Shimon. The mishnah expresses the fact that she is fully betrothed to Shimon by stating that if she is an Israelites daughter and therefore prohibited to eat terumah, she is now fully betrothed to Shimon and if he is a priest she may eat terumah. Were she not fully betrothed, the mishnah would not say that she can eat terumah.
Section three: In this case, Reuven makes an ambiguous statement, Be betrothed to me from now and after thirty days. It is unclear whether his betrothal begins now, or after thirty days. Alternatively, she may begin to be betrothed now but not fully betrothed until thirty days. In any case, if Shimon comes along and betroths her within the thirty days, his kiddushin is also doubtfully valid. If Reuvens betrothal has begun, then she is betrothed to Reuven and Shimons act is irrelevant; but if Reuvens betrothal has not begun, then she would be betrothed to Shimon. Alternatively, if Reuvens betrothal has begun but not been completed, she may be betrothed to both of them at the same time. In such a situation she would be forbidden to both and require a get from both (see Gittin 7:3). If she was the daughter of a priest and one of them was an Israelite, she would no longer eat terumah lest her marriage to that man was valid. Similarly, if she is the daughter of an Israelite and one of the men was a priest she would not eat terumah lest her marriage to that man was not valid. In other words, we act stringently and she doesnt get to eat terumah no matter what the case. Again, this is the mishnahs way of saying that she is doubtfully married to both men and not fully married to either.