Set Complement inverts Subsets

Theorem

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

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

Proof
$$ $$ $$ $$ $$