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

Theorem
Let $S$ be a set.

Let $\family {S_i}_{i \mathop \in I}$ be a family of subsets of $S$.

Then:
 * $\displaystyle \relcomp S {\bigcup_{i \mathop \in I} \mathbb S_i} = \bigcap_{i \mathop \in I} \relcomp S {S_i}$