Set Difference is Right Distributive over Union

Theorem
Set difference is right distributive over union.

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

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

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

Proof
$$ $$ $$