Theorem xrneq12

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

	Ref	Expression
Assertion	xrneq12	$$⊢\left(A=B\wedge C=D\right)\to A⋉C=B⋉D$$

Proof

Step	Hyp	Ref	Expression
1		xrneq1	$$⊢A=B\to A⋉C=B⋉C$$
2		xrneq2	$$⊢C=D\to B⋉C=B⋉D$$
3	1 2	sylan9eq	$$⊢\left(A=B\wedge C=D\right)\to A⋉C=B⋉D$$