If $A, B, C, D$ are sets such that $A \sim B$ and $C \sim D$, $\exists$ bijections $f: A \to B$ and $g: C \to D$. Let $h: A \times C \to B \times D$ be $h(a,c) = (f(a), g(c))$. Show that $h$ is a bijection (and thus $A\times C \sim B \times D$).
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