Cartesian Product of Subsets/Corollary 3

Corollary to Cartesian Product of Subsets
Let $A, B, C$ be sets such that $B \ne \O$.

Let $A \times B \subseteq C \times C$.

Then:
 * $A \subseteq B$

Proof
Since $B \ne O$ we have from Cartesian Product of Subsets that:


 * $A \times B \subseteq C \times C \implies A \subseteq C \land B \subseteq C$