This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem unieqd

Description: Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995)

		Ref	Expression
	Hypothesis	unieqd.1	$⊢ φ \to A = B$
	Assertion	unieqd	$⊢ φ \to ⋃ A = ⋃ B$

Step	Hyp	Ref	Expression
1		unieqd.1	$⊢ φ \to A = B$
2		unieq	$⊢ A = B \to ⋃ A = ⋃ B$
3	1 2	syl	$⊢ φ \to ⋃ A = ⋃ B$