There are other books in the literature that mainly focus on how to go about proving things rather than proving specific things.

Some titles that come up are:

Mathematical Proofs: A transition to Advanced Mathematics by Chartrand, Polimeni and Zhang.

Book of Proof: Richard Hammack

Jay Cumming’s Proofs

I remember I once had a book that advertised itself as a book on Discrete Mathematics but it turned out to be more in line with the titles above, was a gem, if I find it I'll let you know.

But it's nice to see I'm not the only guy who gets a kick out of this stuff.

I wouldn't bother with things from the foundations of mathematics area, like Russel or Frege and whoever else came from that era, back when people still wrote an 800 page treatise on what a "number" even is. A lot of the material coming from that period seems to have been thrown down the drain.

> I remember I once had a book that advertised itself as a book on Discrete Mathematics but it turned out to be more in line with the titles above, was a gem, if I find it I'll let you know.

Every discrete math book I've ever seen has a strong proof component; it's supposed to be an undergraduate's introduction to rigor. The classes taught out of those books may not actually be that rigorous, depending on whether the students are going to be expected to rigorously prove things later, or if it's just Leetcode combinatorics.

But for a guess, maybe Kenneth Rosen?

Ah yes, I think this was it, I see a note that I have the 7th edition and I wanted to get a hold of the 8th.