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Metamath Proof Explorer

Theorem iuneq2d

Description: Equality deduction for indexed union. (Contributed by Drahflow, 22-Oct-2015)

		Ref	Expression
	Hypothesis	iuneq2d.2	$⊢ φ \to B = C$
	Assertion	iuneq2d	$⊢ φ \to ⋃_{x \in A} B = ⋃_{x \in A} C$

Step	Hyp	Ref	Expression
1		iuneq2d.2	$⊢ φ \to B = C$
2	1	adantr	$⊢ (φ \land x \in A) \to B = C$
3	2	iuneq2dv	$⊢ φ \to ⋃_{x \in A} B = ⋃_{x \in A} C$