Cartesian Product of Subsets/Corollary 1

Corollary to Cartesian Product of Subsets
Let $A, B, S$ be sets such that $A \subseteq B$.

Then:
 * $A \times S \subseteq B \times S$

Proof
From Set is Subset of Itself we have $S \subseteq S$.

From Cartesian Product of Subsets:
 * $A \subseteq B \land S \subseteq S \implies A \times S \subseteq B \times S$