Theorem coeq1d

Description: Equality deduction for composition of two classes. (Contributed by NM, 16-Nov-2000)

	Ref	Expression
Hypothesis	coeq1d.1	|- ( ph -> A = B )
Assertion	coeq1d	|- ( ph -> ( A o. C ) = ( B o. C ) )

Proof

Step	Hyp	Ref	Expression
1		coeq1d.1	|- ( ph -> A = B )
2		coeq1	|- ( A = B -> ( A o. C ) = ( B o. C ) )
3	1 2	syl	|- ( ph -> ( A o. C ) = ( B o. C ) )