Set Difference with Set Difference is Union of Set Difference with Intersection/Corollary

Theorem
Let $S$ and $T$ be sets.

Then:
 * $T \setminus \paren {S \setminus T} = T$

where $S \setminus T$ denotes set difference.

Proof
From Set Difference with Set Difference is Union of Set Difference with Intersection:
 * $R \setminus \paren {S \setminus T} = \paren {R \setminus S} \cup \paren {R \cap T}$

where $R, S, T$ are sets.

Hence: