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

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

Then:
 * $\ds \map \complement {\bigcup_{i \mathop \in I} S_i} = \bigcap_{i \mathop \in I} \map \complement {S_i}$