Metamath Proof Explorer

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 |X. C ) = ( B |X. C )

Proof

Step Hyp Ref Expression
1 xrneq1i.1 
 |-  A = B
2 xrneq1 
 |-  ( A = B -> ( A |X. C ) = ( B |X. C ) )
3 1 2 ax-mp 
 |-  ( A |X. C ) = ( B |X. C )