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.