Set Complement inverts Subsets

Theorem
Let $S$ and $T$ be sets.

Then:
 * $S \subseteq T \iff \complement \left({T}\right) \subseteq \complement \left({S}\right)$

where:
 * $S \subseteq T$ denotes that $S$ is a subset of $T$
 * $\complement$ denotes set complement.