Intersection with Set Difference is Set Difference with Intersection

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

Then:
 * $\left({R \setminus S}\right) \cap T = \left({R \cap T}\right) \setminus S$

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