De Morgan's Laws (Set Theory)/Set Complement/Family of Sets/Complement of Union

Theorem
Let $\left\langle{S_i}\right\rangle_{i \in I}$ be a family of sets, all of which are subsets of a universe $\mathbb U$.

Then:
 * $\displaystyle \complement \left({\bigcup_{i \mathop \in I} S_i}\right) = \bigcap_{i \mathop \in I} \complement \left({S_i}\right)$