Indexed Union Equality

Theorem
Let $A$, $B_x$, and $C_x$ be classes. Then:


 * $\displaystyle \forall x \in A: B_x = C_x \implies \bigcup_{x \mathop \in A} B_x = \bigcup_{x \mathop \in A} C_x$

Proof
Proof follows from Indexed Union Subset and definition of set equality.