# Indexed Union Subset

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## Theorem

Let $A$, $B_x$ and $C_x$ be classes.

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Then:

- $\ds \forall x \in A: B_x \subseteq C_x \implies \bigcup_{x \mathop \in A} B_x \subseteq \bigcup_{x \mathop \in A} C_x$

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## Proof

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