Set Intersection is Self-Distributive/General Result

Theorem

Let $\family {\mathbb S_i} _{i \mathop \in I}$ be an $I$-indexed family of sets of sets.

Then:

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


Proof


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