Beitza 12 - Once it is allowed - it is allowed
There are thirty nine labors prohibited on Shabbat, and they are equally prohibited on a Holiday (Yom Tov). However, on Yom Tov one can cook food, and those labors that are needed for this constitute an exception
Beit Shammai nevertheless state that one cannot carry a child or a Torah into the street on a Yom Tov. Why not? Because they are not edible. Beit Hillel allow this. We thus see that Beit Hillel have a rule: once something is permitted for the purposes of cooking, it is permitted for all purposes. But how do we know that this is a general argument and not just one about carrying? - Because they disagree also about lighting the fire: once it is allowed for cooking, Beit Hillel permit it for all other purposes.
When one cooks, she needs to give a portion to a Kohen. Beit Shammai, however, prohibited taking the present to the Kohen: just as one cannot take tithe to Kohen on a Yom Tov, so she cannot take other gifts. What do Beit Hillel answer? They say that it is not the same: tithe cannot be carried because it is cannot be separated; will you say the same about Kohen food gifts, which can be separated? - Of course not.
Art: Girl Carrying a Child by William-Adolphe Bouguereau