Theorem xrneq1i

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

	Ref	Expression
Hypothesis	xrneq1i.1	⊢ 𝐴 = 𝐵
Assertion	xrneq1i	⊢ ( 𝐴 ⋉ 𝐶 ) = ( 𝐵 ⋉ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		xrneq1i.1	⊢ 𝐴 = 𝐵
2		xrneq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ⋉ 𝐶 ) = ( 𝐵 ⋉ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ⋉ 𝐶 ) = ( 𝐵 ⋉ 𝐶 )