# Indexed Union Equality

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## 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.