Theorem oveq12d

Description: Equality deduction for operation value. (Contributed by NM, 13-Mar-1995) (Proof shortened by Andrew Salmon, 22-Oct-2011)

	Ref	Expression
Hypotheses	oveq1d.1	$$⊢\phi \to A=B$$
	oveq12d.2	$$⊢\phi \to C=D$$
Assertion	oveq12d	$$⊢\phi \to AFC=BFD$$

Proof

Step	Hyp	Ref	Expression
1		oveq1d.1	$$⊢\phi \to A=B$$
2		oveq12d.2	$$⊢\phi \to C=D$$
3		oveq12	$$⊢\left(A=B\wedge C=D\right)\to AFC=BFD$$
4	1 2 3	syl2anc	$$⊢\phi \to AFC=BFD$$