Should one include already cemented proofs of related principles in one's paper?

In a paper I’m writing (purely recreationally, nothing fancy), I state that "an odd number minus an odd number = an even number". I also state that "an even number minus an odd number = an odd number".

Now, should I provide the proof for this in the last section of my paper? And if so, is there a standard proof?

I was thinking Euclid’s proof, but perhaps there is a standard proof for every principle or axiom (or whatever one would call it). Maybe Euclid’s proof is the standard?