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

Metamath Proof Explorer

Theorem xrneq1d

Description: Equality theorem for the range Cartesian product, deduction form. (Contributed by Peter Mazsa, 7-Sep-2021)

		Ref	Expression
	Hypothesis	xrneq1d.1	$⊢ φ \to A = B$
	Assertion	xrneq1d	$⊢ φ \to A ⋉ C = B ⋉ C$

Step	Hyp	Ref	Expression
1		xrneq1d.1	$⊢ φ \to A = B$
2		xrneq1	$⊢ A = B \to A ⋉ C = B ⋉ C$
3	1 2	syl	$⊢ φ \to A ⋉ C = B ⋉ C$