Cartesian Product of Subsets/Corollary 2

Corollary to Cartesian Product of Subsets

Let $A, S, T$ be sets such that $S \subseteq T$.

Then:

$A \times S \subseteq A \times T$

Proof

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

From Cartesian Product of Subsets:

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

$\blacksquare$