Theorem oveq123d

Description: Equality deduction for operation value. (Contributed by FL, 22-Dec-2008)

	Ref	Expression
Hypotheses	oveq123d.1	|- ( ph -> F = G )
	oveq123d.2	|- ( ph -> A = B )
	oveq123d.3	|- ( ph -> C = D )
Assertion	oveq123d	|- ( ph -> ( A F C ) = ( B G D ) )

Proof

Step	Hyp	Ref	Expression
1		oveq123d.1	|- ( ph -> F = G )
2		oveq123d.2	|- ( ph -> A = B )
3		oveq123d.3	|- ( ph -> C = D )
4	1	oveqd	|- ( ph -> ( A F C ) = ( A G C ) )
5	2 3	oveq12d	|- ( ph -> ( A G C ) = ( B G D ) )
6	4 5	eqtrd	|- ( ph -> ( A F C ) = ( B G D ) )