How do you prove by algebra that if you add two even numbers you get an even number?

You use the definition of even numbers which says it is a number of the form 2n for some integer n, and you take two of them, say 2n and 2m and add them and see that you have 2n+2m=2(n+m) and since n and m are integers so is n+m so lets call it p so the sum is 2p and this is even by definition of even numbers