Theorem oveq12i

Description: Equality inference for operation value. (Contributed by NM, 28-Feb-1995) (Proof shortened by Andrew Salmon, 22-Oct-2011)

	Ref	Expression
Hypotheses	oveq1i.1	⊢ 𝐴 = 𝐵
	oveq12i.2	⊢ 𝐶 = 𝐷
Assertion	oveq12i	⊢ ( 𝐴 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐷 )

Proof

Step	Hyp	Ref	Expression
1		oveq1i.1	⊢ 𝐴 = 𝐵
2		oveq12i.2	⊢ 𝐶 = 𝐷
3		oveq12	⊢ ( ( 𝐴 = 𝐵 ∧ 𝐶 = 𝐷 ) → ( 𝐴 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐷 ) )
4	1 2 3	mp2an	⊢ ( 𝐴 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐷 )