Theorem xrneq1d

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

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

Proof

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