ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4163 on D76: Set intersection
Subset of binary intersection iff subset of both sets in the intersection
Formulation 0
Let $X, A, B$ each be a D11: Set such that
(i) $A \cap B$ is the D76: Set intersection of $A$ and $B$
Then \begin{equation} X \subseteq A \cap B \quad \iff \quad X \subseteq A, \; X \subseteq B \end{equation}