Set Difference with Union is Set Difference

Theorem
The set difference between two sets is the same as the set difference between their union and the second of the two sets:

Let $S, T$ be sets.

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

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