Metamath Proof Explorer

Theorem fvoveq1

Description: Equality theorem for nested function and operation value. Closed form of fvoveq1d . (Contributed by AV, 23-Jul-2022)

Ref Expression
Assertion fvoveq1 
|- ( A = B -> ( F ` ( A O C ) ) = ( F ` ( B O C ) ) )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( A = B -> A = B )
2 1 fvoveq1d 
 |-  ( A = B -> ( F ` ( A O C ) ) = ( F ` ( B O C ) ) )