If you want to go deeply into formalized mathematics, take a look at the Metamath Proof Explorer <https://us.metamath.org/mpeuni/mmset.html https://us.metamath.

If you want to go deeply into formalized mathematics, take a look at the Metamath Proof Explorer <https://us.metamath.org/mpeuni/mmset.html https://us.metamath.org/mpeuni/mmset.html>. It defines a set of axioms, and formally verifies every proof showing every step (hiding nothing).