Kiddushin 41B

פיחת עשרה או הוסיף עשרה ⁠– תרומתו תרומה. מנלן? וכי תימא דיליף מגירושין ⁠– מה לגירושין, שכן ישנן חול! אמר קרא: ״אתם״, ״גם אתם״⁠ – לרבות את השליח.

If the agent subtracted 10 from the denominator and separated 1/40th or added 10 to the denominator and separated 1/60th, thereby giving more or less than the owner intended, his teruma is teruma. From where do we derive that one can appoint an agent to separate teruma? And if you would say that it is derived from divorce, one could argue: What is an aspect unique to divorce is that it is considered a non-sacred matter in relation to teruma and will have different halakhot, so one cannot learn from divorce that one can appoint an agent to separate teruma. The Talmud answers: The verse states with regard to teruma: “So you also should set apart a gift to YHWH of all your tithes” (Numbers 18:28). Once the verse states “you,” the addition of the word “also” in the term “you also” serves to include an agent.

ונכתוב רחמנא בתרומה, וניתו הנך ונגמרו מיניה! משום דאיכא למפרך: שכן ישנה במחשבה.

The Talmud asks: And let God write in the passage concerning teruma that one can appoint an agent, and the halakha that one can appoint an agent to act on his behalf in these other matters, i.e., divorce and betrothal, can come and be derived from it. The Talmud answers: Agency in these matters cannot be derived in this manner because the derivation can be refuted: Separating teruma is different, in that it is able to be separated by mere thought. It is enough for one to decide that a certain portion of his produce should be teruma to have that status take effect. Just as there is this leniency unique to separating teruma, perhaps the leniency that enables one to appoint an agent is also unique to separating teruma.