Theorem ineq1d

Description: Equality deduction for intersection of two classes. (Contributed by NM, 10-Apr-1994)

	Ref	Expression
Hypothesis	ineq1d.1	|- ( ph -> A = B )
Assertion	ineq1d	|- ( ph -> ( A i^i C ) = ( B i^i C ) )

Proof

Step	Hyp	Ref	Expression
1		ineq1d.1	|- ( ph -> A = B )
2		ineq1	|- ( A = B -> ( A i^i C ) = ( B i^i C ) )
3	1 2	syl	|- ( ph -> ( A i^i C ) = ( B i^i C ) )