1.) Show addition in the reals is well defined. i.e. $\displaystyle x=y\implies x+a=y+a $ for $\displaystyle x,y,a\in\mathbb{R} $.

2.) Given a set $\displaystyle S $, choose $\displaystyle (x,y), (w,z)\in S\times S $.

Show $\displaystyle (x,y)=(w,z)\iff x=w $ and $\displaystyle y=z $.