P.S. Come to think of it, there's another aspect I don't understand. The validity of a theorem depends only on the assumptions used in the proof (so, for examp

P.S. Come to think of it, there's another aspect I don't understand. The validity of a theorem depends only on the assumptions used in the proof (so, for example, if I have a formal set theory proof that depends only on group axioms, then it applies to all groups). That is not a property that is usually expressible in the the logic -- it's a property of the proof theory of the logic -- but it is nevertheless true. Not being a logician, I'm not interested in writing proofs about my logic's proof theory, I don't need to define new proof rules as I don't develop new logics, and my logic's proof assistant is free to rely on theorems about the logic's proof theory. What do I, as a practitioner, gain by making the proof theory part of the logic?