Theorem xrneq1d

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

	Ref	Expression
Hypothesis	xrneq1d.1	|- ( ph -> A = B )
Assertion	xrneq1d	|- ( ph -> ( A |X. C ) = ( B |X. C ) )

Proof

Step	Hyp	Ref	Expression
1		xrneq1d.1	|- ( ph -> A = B )
2		xrneq1	|- ( A = B -> ( A |X. C ) = ( B |X. C ) )
3	1 2	syl	|- ( ph -> ( A |X. C ) = ( B |X. C ) )