Metamath Proof Explorer

Theorem coideq

Description: Equality theorem for composition of two classes. (Contributed by Peter Mazsa, 23-Sep-2021)

Ref Expression
Assertion coideq 
|- ( A = B -> ( A o. A ) = ( B o. B ) )

Proof

Step Hyp Ref Expression
1 coeq1 
 |-  ( A = B -> ( A o. A ) = ( B o. A ) )
2 coeq2 
 |-  ( A = B -> ( B o. A ) = ( B o. B ) )
3 1 2 eqtrd 
 |-  ( A = B -> ( A o. A ) = ( B o. B ) )