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A Kohen who eats Terumah mid'Rabanan is not regarded as a Kohen with regard to Yuchsin, even according to the opinion that says "Ma'alim mi'Terumah l'Yuchsin."
A Bas Kohen who is widowed from a Yisrael returns to her father's home for the purpose of eating Terumah but not for the purpose of eating Kodshim.
Nesi'us Kapayim in Bavel, eating Chalah in Surya, and receiving the Matnos Kehunah in the cities is a Chazakah for Kehunah. (1)
Nesi'us Kapayim is a Chazakah for Kehunah in all places within reach of the agents of Beis Din. (2)
According to the Rabanan d'Vei Rav, the Mitzvah of Chalah nowadays is mid'Oraisa. (3)
Rav Huna bar Yehoshua: Chalah nowadays is only a Mitzvah mid'Rabanan. (4)
If a person is called up first to the Torah and he is followed by a Levi, it is sufficient proof that he is a Kohen. (5)
If a person is called up second to the Torah following a Kohen, it is sufficient proof that that he is a Levi.
Rebbi: A father is believed that his son is a Kohen regarding Terumah, but not regarding marriage. (6)
A BIT MORE
1. If a person has a Chazakah on any of these things, he is regarded as a Kohen and he may eat Terumah mid'Oraisa.
2. Any place within fifteen days' of travel time from Eretz Yisrael was within reach of the agents of the Beis Din, who were sent out in order to notify the people about the new month. All of the places within fifteen days of Eretz Yisrael had a Beis Din that would receive the agents, and since there was a Beis Din there they checked into the lineage of the residents and would not allow a non-Kohen to do Nesi'us Kapayim. If somebody did Nesi'us Kapayim, we can be sure that he is a Kohen.
3. Even according to the opinion that Terumah nowadays is mid'Rabanan, Chalah is mid'Oraisa because the first fourteen years in Eretz Yisrael -- while Klal Yisrael was conquering and dividing up the land -- the obligation of Chalah applied but not the obligation of Terumah.
4. Even according to the opinion that Terumah nowadays is mid'Oraisa, Chalah is mid'Rabanan because the obligation of Chalah applies only when all of Klal Yisrael is in Eretz Yisrael.
5. However, if a Levi was not called up after him, there is no proof that he is a Kohen, because perhaps no Kohen was present and they called him up first because he was the most prominent member of the congregation.
6. He is believed regarding Terumah because it is in his hands to feed him Terumah, but he is not believed regarding marriage because it is not in his hands to marry him off.
THE MITZVAH OF CHALAH IN PRESENT TIMES
Rav Huna bar Yehoshua maintains that Chalah nowadays is only a Mitzvah mid'Rabanan, because the obligation of Chalah is only when all of Klal Yisrael is in Eretz Yisrael. The Minchas Chinuch says that even though, toward the end of the period of the second Beis ha'Mikdash, the ten Shevatim had already been exiled and most of Klal Yisrael no longer lived in Eretz Yisrael, the Mitzvah of Chalah continued to apply. When Rav Huna bar Yehoshua says that Chalah applies only when all of Klal Yisrael is in Eretz Yisrael, he means when Eretz Yisrael has been conquered by all of Klal Yisrael such as in the times of Yehoshua bin Nun. Since Eretz Yisrael was conquered by all of Klal Yisrael, the Mitzvah of Chalah applies even after most of Klal Yisrael no longer lives there. However, once Yehudah and Binyamin were exiled, the sanctity of Eretz Yisrael was negated and the Mitzvah of Chalah no longer applied. Even though Eretz Yisrael was reconquered at the time of Ezra and regained its sanctity, since it was not conquered by all of Klal Yisrael the Mitzvah of Chalah does not apply.
THE MITZVAH OF CHALAH
The obligation to separate Chalah applies only in Eretz Yisrael, and only when all of Klal Yisrael is living there. Therefore, Chalah nowadays (and even at the time of Ezra) is only mid'Rabanan. We must separate Chalah in Chutz la'Aretz mid'Rabanan so that the Mitzvah of Chalah will not be forgotten in Klal Yisrael. (Shulchan Aruch YD 322:2-3)
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