Set Difference with Set Difference is Union of Set Difference with Intersection

Theorem
Let $R, S, T$ be sets.

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

where:
 * $S \setminus T$ denotes set difference
 * $S \cup T$ denotes set union
 * $S \cap T$ denotes set intersection.

Proof
Consider $R, S, T \subseteq \mathbb U$, where $\mathbb U$ is considered as the universe.