Complement of Complement

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


 * $\complement \paren {\complement \paren S} = S$

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