Intersection is Subset/Family of Sets

Theorem
Let $\left \langle{S_i}\right \rangle_{i \in I}$ be a family of sets indexed by $I$.

Then:
 * $\displaystyle \forall i \in I: \bigcap_{j \mathop \in I} S_j \subseteq S_i$

where $\displaystyle \bigcap_{j \mathop \in I} S_j$ is the intersection of $\left \langle{S_j}\right \rangle$.