The question:

x,y integers, 0 < x < y ==> x^2< y^2

I used closure of the positive integers to show that x^2 and y^2 are both greater than 0.

Before this question, I proved a few statements involving the transitivity of the < relation. I can prove the statement above quite easily using the induction postulate for the positive integers, but I would like to see a proof involving the transitivity of the order relation as I can't seem to come up with one on my own. Thanks.