Theorem ineqan12d

Description: Equality deduction for intersection of two classes. (Contributed by NM, 7-Feb-2007)

	Ref	Expression
Hypotheses	ineq1d.1	|- ( ph -> A = B )
	ineqan12d.2	|- ( ps -> C = D )
Assertion	ineqan12d	|- ( ( ph /\ ps ) -> ( A i^i C ) = ( B i^i D ) )

Proof

Step	Hyp	Ref	Expression
1		ineq1d.1	|- ( ph -> A = B )
2		ineqan12d.2	|- ( ps -> C = D )
3		ineq12	|- ( ( A = B /\ C = D ) -> ( A i^i C ) = ( B i^i D ) )
4	1 2 3	syl2an	|- ( ( ph /\ ps ) -> ( A i^i C ) = ( B i^i D ) )