Set Difference is Right Distributive over Set Intersection/General Case

Theorem
Let $U$ be a collection of sets, and let $T$ be a set.

Then $$\bigcap_{X\in U}(X\setminus T)=\left(\bigcap_{T\in U} X\right)\setminus T$$ i.e. the difference of an intersection of sets is equale the intersection of the differences.