Metamath Proof Explorer

Theorem xpeq2i

Description: Equality inference for Cartesian product. (Contributed by NM, 21-Dec-2008)

Ref Expression
Hypothesis xpeq1i.1 
|- A = B
Assertion xpeq2i 
|- ( C X. A ) = ( C X. B )

Proof

Step Hyp Ref Expression
1 xpeq1i.1 
 |-  A = B
2 xpeq2 
 |-  ( A = B -> ( C X. A ) = ( C X. B ) )
3 1 2 ax-mp 
 |-  ( C X. A ) = ( C X. B )