Metamath Proof Explorer


Theorem oveq

Description: Equality theorem for operation value. (Contributed by NM, 28-Feb-1995)

Ref Expression
Assertion oveq ⊢ F = G → A F B = A G B

Proof

Step Hyp Ref Expression
1 fveq1 ⊢ F = G → F ⁡ A B = G ⁡ A B
2 df-ov ⊢ A F B = F ⁡ A B
3 df-ov ⊢ A G B = G ⁡ A B
4 1 2 3 3eqtr4g ⊢ F = G → A F B = A G B