Relative Complement inverts Subsets

Theorem
Let $T_1, T_2 \subseteq S$.

Then:
 * $T_1 \subseteq T_2 \iff \complement_S \left({T_2}\right) \subseteq \complement_S \left({S}\right)$

where:
 * $T_1 \subseteq T_2$ denotes that $T_1$ is a subset of $T_2$
 * $\complement_S$ denotes complement relative to $S$.