Theorem xrneq2i

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

	Ref	Expression
Hypothesis	xrneq2i.1	⊢ 𝐴 = 𝐵
Assertion	xrneq2i	⊢ ( 𝐶 ⋉ 𝐴 ) = ( 𝐶 ⋉ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		xrneq2i.1	⊢ 𝐴 = 𝐵
2		xrneq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 ⋉ 𝐴 ) = ( 𝐶 ⋉ 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐶 ⋉ 𝐴 ) = ( 𝐶 ⋉ 𝐵 )