Prove or give a counter example. $\displaystyle A \subseteq C, B \subseteq D \to A \times B \subseteq C \times D$

I said

True.

let $\displaystyle x \in A$ then $\displaystyle x \in C$

let $\displaystyle y \in A$ then $\displaystyle y \in C$

$\displaystyle (x,y) \in C \times D$

is that enough of a proof?