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Part of https://groups.google.com/g/metamath/c/OB2_9sYgDfA.
Now it comes the truly systematic phase: reducing ax-13 usage with the minimizer.
Each PR will be the result of the scan of 50 theorems, so at most you'll see 50 changed proofs per PR.
I created a new branch named "all", containing the combination of future minimizations. In the "all" branch ax-13 is used by only 3517 proofs (currently ax-13 is used by 25,000 proofs). It is not as good as ax-13-complete, but we shouldn't worry too much about it, because once ax-13 usage will be low it will be easier to identify the "missing chains" to bring that number even lower.
Each change obeys the following criteria:
A change must drop ax-13 from the theorem whose proof is edited. If a proof is edited without its dependency on ax-13 reduced, then it's either the result of a recompression (so a shortening) or a mistake (I've never seen it so far).
A change replaces the use of a theorem with its version with more dv, so the general proof length and shape will stay the same.
This PR drops ax-13 from 61 theorems. Full axiom usage here: f489ed8