# Indexed Union Equality

Jump to navigation
Jump to search

## 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.