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 ) )