Set Difference is Right Distributive over Set Intersection

Theorem
Set difference is right distributive over set intersection.

Let $R, S, T$ be sets.

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

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

Proof 1
Consider $R, S, T \subseteq \mathbb U$, where $\mathbb U$ is considered as the universe.