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Metamath Proof Explorer

Theorem iuneq2i

Description: Equality inference for indexed union. (Contributed by NM, 22-Oct-2003)

		Ref	Expression
	Hypothesis	iuneq2i.1	$⊢ x \in A \to B = C$
	Assertion	iuneq2i	$⊢ ⋃_{x \in A} B = ⋃_{x \in A} C$

Step	Hyp	Ref	Expression
1		iuneq2i.1	$⊢ x \in A \to B = C$
2		iuneq2	$⊢ \forall x \in A B = C \to ⋃_{x \in A} B = ⋃_{x \in A} C$
3	2 1	mprg	$⊢ ⋃_{x \in A} B = ⋃_{x \in A} C$