Q:

Inequality + Sets Proof

Let x,y,z be sets in universe U
if  $x\subseteq$ y, then  $x-z\subseteq y-z$  
How to prove this formally?

A:

Let $p \in x-z$, that is $p \in x$ and $p \notin z$.
It suffices to prove that $p \in y$, are you able to complete the proof?

