Set Difference with Set Difference

Theorem
The set difference with the set difference of two sets is the intersection of the two sets:
 * $S \setminus \left({S \setminus T}\right) = S \cap T = T \setminus \left({T \setminus S}\right)$

Proof
Interchanging $S$ and $T$:
 * $T \setminus \left({T \setminus S}\right) = T \cap S$

from which the other half of the equality follows from the fact that Intersection is Commutative.