I was wondering if anyone is aware of a modern book that builds a subset of elementary number theory from Peano axioms preferably in a Principia Mathematica fashion?
Or similarly an encyclopedia of mathematical proofs in some branches of mathematics only using the language of first-order logic and ZFC but not the English language.
Wiki proofs is an encyclopedia of proofs for example, but you cannot feed it to a computer program for example.
using a web search, this one looks interesting and maybe meets your needs:
http://us.metamath.org/mpegif/mmset.html