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If the handful of flour from one offering became mixed with the handful from another offering, or with the flour offering of a regular kohen, or with the daily offering of the High Priest, they are all still valid and can be burned on the Altar. Rabbi Yehudah disagrees with regard to the High Priest's offering, which contains three times as much oil. Since it is loose like batter, it will mix with our less oily handful and nullify it.
But Rabbi Yehudah's own opinion everywhere in the Talmud is that like substances never nullify each other, so how can he rule differently here? He will answer that our case is different: we view the oil in our handful as if not present, and then the oil in the High Priest's offering nullifies our flour.
We explore the halachic ramifications of min bemino.