Relative Complement of Relative Complement

Theorem
The relative complement of the relative complement of a set is itself:
 * $\relcomp S {\relcomp S T} = T$

Thus, considered as a mapping on the power set of $S$:
 * $\complement_S: \powerset S \to \powerset S: \relcomp S T = S \setminus T$

$\complement_S$ is an involution.