De Morgan's Laws (Set Theory)/Set Complement/General Case

Theorem
Let $\mathbb T$ be a set of sets, all of which are subsets of a universe $\mathbb U$.

Then:
 * $(1): \quad \displaystyle \complement \left({\bigcap \mathbb T}\right) = \bigcup_{H \mathop \in \mathbb T} \complement \left({H}\right)$


 * $(2): \quad \displaystyle \complement \left({\bigcup \mathbb T}\right) = \bigcap_{H \mathop \in \mathbb T} \complement \left({H}\right)$