Set Difference with Union

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

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

where:
 * $R \setminus S$ denotes set difference;
 * $R \cup T$ denotes set union.

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

Then:

Then of course: