Midrash for Chullin 264:3
השוחט לכהן ולעובד כוכבים פטור מן המתנות:
Why does not the Mishnah teach simply.'
Sifrei Devarim
"from the people": and not from others (i.e., gentiles), and not from his fellow Cohanim.
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Talmud Bavli