Theorem xrneq2d

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

	Ref	Expression
Hypothesis	xrneq2d.1	|- ( ph -> A = B )
Assertion	xrneq2d	|- ( ph -> ( C |X. A ) = ( C |X. B ) )

Proof

Step	Hyp	Ref	Expression
1		xrneq2d.1	|- ( ph -> A = B )
2		xrneq2	|- ( A = B -> ( C |X. A ) = ( C |X. B ) )
3	1 2	syl	|- ( ph -> ( C |X. A ) = ( C |X. B ) )