We are learning Maseches Yevamos, chapter 7, mishnah 3, which deals with the share a fetus holds in slaves and the implications for whether the slaves of a widow may eat Terumah.
The text of the mishnah:
"Bas Yisrael shenises l'kohen, umeis, v'hinicha me'uberes - lo yochlu avadeha bi'terumah, mipnei chelko shel ubar" - The case is a daughter of a Yisrael who married a kohen, and her husband the kohen died and left her pregnant. The scenario is that in addition to the fetus in her womb, she already has children from that same kohen. Her slaves - meaning slaves of the tzon barzel category - do not eat Terumah, because of the share in those slaves that is owned by the fetus in her womb. For the fetus too has a share in the slaves, exactly like his living brothers who hold a share in them.
"Ha'ubar posel v'eino ma'achil" - the fetus disqualifies but does not enable eating:
It disqualifies - a daughter of a kohen who married a Yisrael and whose husband died normally returns to her father's house and eats Terumah; but if she is pregnant from her Yisrael husband, the fetus disqualifies her from eating.
And it does not enable eating - in the reverse case, a daughter of a Yisrael married to a kohen: her children enable her to eat Terumah, as stated at the beginning of the mishnah, but the fetus itself does not enable anyone else to eat, including the slaves. And not only does it fail to enable them to eat, it actually prevents them from eating.
These are the words of Rabbi Yosei: the fetus does not permit the slaves to eat, and since it has a share in them - they too do not eat.
Between tzon barzel slaves and melog slaves:
Tzon barzel slaves - these are owned by the husband or his heirs, such as his children, including the fetus. These slaves do not eat because of the share of the fetus.
Melog slaves - these belong to her. Since she has other children and she herself eats Terumah, they eat as well.
The claim of the Chachamim:
"Me'achar she'he'adeta lanu al bas Yisrael l'kohen, af bas kohen l'kohen umeis v'hinicha me'uberes - lo yochlu avadeha bi'terumah, mipnei chelko shel ubar" - that is: since you have already testified before us regarding a daughter of a Yisrael married to a kohen who died and left her pregnant, that the tzon barzel slaves do not eat because of the share of the fetus, then that very same ruling should apply also to a daughter of a kohen who married a kohen and he died and left her pregnant - that there too the slaves do not eat Terumah because of the share of the fetus in her womb, since part of those slaves is owned by him and he does not allow them to eat.
Rabbi Yosei stated his ruling only regarding a daughter of a Yisrael who married a kohen, while the Chachamim point out that the ruling should hold true even for a daughter of a kohen married to a kohen. The basis of the dispute lies in the reason behind his words, and the Gemara brings two possible reasons for Rabbi Yosei's position:
"Ubar bi'm'ei zarah zar hu" - a fetus located in the womb of a woman who is a zarah, who is not the daughter of a kohen, is itself considered a zar, and its status as a zar prevents the slaves from eating Terumah, since it owns a share of them. According to this reason, the ruling is relevant only when she is the daughter of a Yisrael, and not when she is the daughter of a kohen.
Only one who has been born enables eating - Rabbi Yosei holds that only one who has been born has the power to enable others to eat Terumah, and therefore one who has not yet been born cannot enable eating.
From the response of the Chachamim to Rabbi Yosei it is evident that they understood his words according to the second reason. For if his reason were that a fetus in the womb of a zarah is a zar, the ruling would not apply at all to a daughter of a kohen. Rather, it is because only one who has been born has the power to enable another person to eat, such as slaves, and one who has not been born does not enable eating - and therefore even when the fetus is in the womb of a daughter of a kohen, the very fact that it owns part of the slaves prevents them from being able to eat Terumah.
In summary: In this mishnah we learned the principle that the fetus disqualifies but does not enable eating, and the opinion of Rabbi Yosei that the tzon barzel slaves of a kohen's widow who was left pregnant do not eat Terumah because of the fetus's share in them, while the melog slaves do eat through her. We examined the two possible reasons behind his opinion - "Ubar bi'm'ei zarah zar hu" or that only one who has been born enables eating - and saw that from the claim of the Chachamim, who extend the ruling even to a daughter of a kohen who married a kohen, it is evident that they understood his reason to be based on the requirement of having been born.