Complement of Complement

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


 * $\complement \left({\complement \left({S}\right)}\right) = S$

Proof
Substitute $\mathbb U$ for $S$ and $S$ for $T$ in $\complement_S \left({\complement_S \left({T}\right)}\right) = T$ from Relative Complement of Relative Complement.