Set Difference with Self is Empty Set

Theorem
The set difference of a set with itself is the empty set:


 * $$S \setminus S = \varnothing$$

Proof
From Subset of Itself:
 * $$S \subseteq S$$

From Set Difference with Superset is Empty Set‎ we have:
 * $$S \subseteq T \iff S \setminus T = \varnothing$$

Hence the result.