Could someone tell me if I proved this correctly?

prove that for all integers m and n, if m and n are odd, then m + n is even.

p: m and n is odd

q: m+n is even(conclusion)

There exists an integer, k[1], such that m = 2 k[1] + 1

There exist an integer, k[2], such that n = 2 k[2] + 1

m + n is even

m + n = k[1]+1 + 2 k[2]+1 = 2(k[1]+k[2])+2