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Metamath Proof Explorer

Theorem iuneq1d

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

		Ref	Expression
	Hypothesis	iuneq1d.1	$⊢ φ \to A = B$
	Assertion	iuneq1d	$⊢ φ \to ⋃_{x \in A} C = ⋃_{x \in B} C$

Step	Hyp	Ref	Expression
1		iuneq1d.1	$⊢ φ \to A = B$
2		iuneq1	$⊢ A = B \to ⋃_{x \in A} C = ⋃_{x \in B} C$
3	1 2	syl	$⊢ φ \to ⋃_{x \in A} C = ⋃_{x \in B} C$