Metamath Proof Explorer


Theorem afv2eq1

Description: Equality theorem for function value, analogous to fveq1 . (Contributed by AV, 4-Sep-2022)

Ref Expression
Assertion afv2eq1 ( 𝐹 = 𝐺 → ( 𝐹 '''' 𝐴 ) = ( 𝐺 '''' 𝐴 ) )

Proof

Step Hyp Ref Expression
1 id ( 𝐹 = 𝐺𝐹 = 𝐺 )
2 eqidd ( 𝐹 = 𝐺𝐴 = 𝐴 )
3 1 2 afv2eq12d ( 𝐹 = 𝐺 → ( 𝐹 '''' 𝐴 ) = ( 𝐺 '''' 𝐴 ) )