# Intersection Distributes over Intersection/General Result

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## Theorem

Let $\left\langle{\mathbb S_i}\right\rangle_{i \in I}$ be an $I$-indexed family of sets of sets.

Then:

$\displaystyle \bigcap_{i \mathop \in I} \bigcap \mathbb S_i = \bigcap \bigcap_{i \mathop \in I} \mathbb S_i$