Theorem xrneq2d

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

	Ref	Expression
Hypothesis	xrneq2d.1	$$⊢\phi \to A=B$$
Assertion	xrneq2d	$$⊢\phi \to C⋉A=C⋉B$$

Proof

Step	Hyp	Ref	Expression
1		xrneq2d.1	$$⊢\phi \to A=B$$
2		xrneq2	$$⊢A=B\to C⋉A=C⋉B$$
3	1 2	syl	$$⊢\phi \to C⋉A=C⋉B$$