Oh man, that resonates with me. One of the constant frustrations for me was that once you get foundations in a topic, the rest follows, but the foundations are

Oh man, that resonates with me. One of the constant frustrations for me was that once you get foundations in a topic, the rest follows, but the foundations are often full of things that are axioms under one metatheory and theorems under another metatheory. When they were axioms, I remember always being comfortable, like "sure I can assume things," but as theorems there's always that bit of "wait hold up you can't just do that without saying more." The one that I remember most strongly that way was the unique mapping from the empty set/object/whatever as a theorem.