Cartesian Product of Subsets/Corollary 1

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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:

$A \subseteq B \land S \subseteq S \implies A \times S \subseteq B \times S$

$\blacksquare$


Sources