Cartesian Product of Subsets/Corollary 3
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Corollary to Cartesian Product of Subsets
Let $A, B, C$ be sets such that $B \ne \O$.
Let $A \times B \subseteq C \times C$.
- $A \subseteq B$
Since $B \ne O$ we have from Cartesian Product of Subsets that:
- $A \times B \subseteq C \times C \implies A \subseteq C \land B \subseteq C$