Complement of Complement

Theorem

The complement of the complement of a set is the set itself:

$\map \complement {\map \complement S} = S$

Proof

Substitute $\mathbb U$ for $S$ and $S$ for $T$ in $\relcomp S {\relcomp S T} = T$ from Relative Complement of Relative Complement.

$\blacksquare$