Proving x + y is rational

Question

I was given the proposition, ∃x,y ∈ R, x is irrational and y is irrational and x+y is rational To prove this, I first converted it into an if statement since it would make it easier to prove. I got, If -(∃x,y ∈ R, if X and y are irrational then X + y is irrational). From what I know, if I prove that the statement inside the brackets is false, by negating it, it would prove that the original proposition is true. However, I can't think of a way to prove this. Can someone help me out?