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Metamath Proof Explorer

Theorem oveq

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

		Ref	Expression
	Assertion	oveq	$⊢ F = G \to A F B = A G B$

Step	Hyp	Ref	Expression
1		fveq1	$⊢ F = G \to F (⟨A, B⟩) = G (⟨A, B⟩)$
2		df-ov	$⊢ A F B = F (⟨A, B⟩)$
3		df-ov	$⊢ A G B = G (⟨A, B⟩)$
4	1 2 3	3eqtr4g	$⊢ F = G \to A F B = A G B$