User blog comment:LittlePeng9/Addition is commutative/@comment-5307762-20141008111228/@comment-1605058-20180306140612

I have phrased it weirdly in the post - PA has six axioms and one axiom schema, I have used two out of the six axioms and three instances of the induction schema. I have no idea if and how using the remaining axioms make the proof any shorter.