Tosefta for Ketubot 50:2
ת"ש חזקה לכהונה נשיאות כפים וחילוק גרנות ועדות עדות חזקה היא אלא לאו הכי קאמר נשיאות כפים כי עדות מה עדות ליוחסין אף נשיאות כפים ליוחסין לא עדות הבאה מכח חזקה כחזקה
Come and hear: A presumption for the priesthood [is constituted by] the “lifting up of the hands” and taking a share at the threshing floors and testimony. Now is testimony a presumption? Rather this is what he means: The “lifting up of the hands is like a testimony:” Just as testimony [raises one] to the status of a priest, so too the “lifting up of the hands’ [raises one] to the status of a priest! No. Testimony that comes on the strength of a presumption is like a presumption.
Tosefta Peah
Rabbi Shimon ben Gamliel says, "Just as the the presumptive status for the priesthood [is established by] the distribution of Terumah on the threshing floors (following Ketubot 25b:2, Steinsaltz tr.), so too, is the presumptive status for the Levites [established by] the distribution of the first tithe on the threshing floors. [However,] the distribution in the court does not [establish] for him the presumption of the priesthood (Ketubot 26a:7).
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Tosefta Peah
There are two presumptions [to establish a putative Kohen's status in the priesthood] in the Land of Israel: the Lifting of the Hands [for the Priestly Benediction] and the distribution [of Terumah] on the threshing floors (see Ketubot 25b:2). And in Syria, and until the places that the messengers of the new month would arrive (Rosh Hashanah 1:3), [a putative Kohen's status is established by] the Lifting of the Hands, but not by the distribution [of Terumah] on the threshing floors. And Bavel is like Syria. Rabbi Shimon ben Elazar says, "So too, in Alexandria, in earlier times when it had a [Jewish] court."
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