Set Difference is Right Distributive over Set Intersection/General Case

Theorem
Let $U$ be a collection of sets.

Let $T$ be a set.

Then:
 * $\ds \bigcap_{X \mathop \in U} \paren {X \setminus T} = \paren {\bigcap_{X \mathop \in U} X} \setminus T$

That is, the difference with an intersection equals the intersection of the differences.