Theorem oveq2

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

	Ref	Expression
Assertion	oveq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 𝐹 𝐴 ) = ( 𝐶 𝐹 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		opeq2	⊢ ( 𝐴 = 𝐵 → ⟨ 𝐶 , 𝐴 ⟩ = ⟨ 𝐶 , 𝐵 ⟩ )
2	1	fveq2d	⊢ ( 𝐴 = 𝐵 → ( 𝐹 ‘ ⟨ 𝐶 , 𝐴 ⟩ ) = ( 𝐹 ‘ ⟨ 𝐶 , 𝐵 ⟩ ) )
3		df-ov	⊢ ( 𝐶 𝐹 𝐴 ) = ( 𝐹 ‘ ⟨ 𝐶 , 𝐴 ⟩ )
4		df-ov	⊢ ( 𝐶 𝐹 𝐵 ) = ( 𝐹 ‘ ⟨ 𝐶 , 𝐵 ⟩ )
5	2 3 4	3eqtr4g	⊢ ( 𝐴 = 𝐵 → ( 𝐶 𝐹 𝐴 ) = ( 𝐶 𝐹 𝐵 ) )