Relative Complement inverts Subsets

Theorem
Let $S$ be a set.

Let $A \subseteq S, B \subseteq S$ be subsets of $S$.

Then:


 * $A \subseteq B \iff \complement_S \left({B}\right) \subseteq \complement_S \left({A}\right)$

where $\complement_S$ denotes the complement relative to $S$.