Theorem xrneq12i

Description: Equality theorem for the range Cartesian product, inference form. (Contributed by Peter Mazsa, 16-Dec-2020)

	Ref	Expression
Hypotheses	xrneq12i.1	$$⊢A=B$$
	xrneq12i.2	$$⊢C=D$$
Assertion	xrneq12i	$$⊢A⋉C=B⋉D$$

Proof

Step	Hyp	Ref	Expression
1		xrneq12i.1	$$⊢A=B$$
2		xrneq12i.2	$$⊢C=D$$
3		xrneq12	$$⊢\left(A=B\wedge C=D\right)\to A⋉C=B⋉D$$
4	1 2 3	mp2an	$$⊢A⋉C=B⋉D$$