Theorem ineq12d

Description: Equality deduction for intersection of two classes. (Contributed by NM, 24-Jun-2004) (Proof shortened by Andrew Salmon, 26-Jun-2011)

	Ref	Expression
Hypotheses	ineq1d.1	|- ( ph -> A = B )
	ineq12d.2	|- ( ph -> C = D )
Assertion	ineq12d	|- ( ph -> ( A i^i C ) = ( B i^i D ) )

Proof

Step	Hyp	Ref	Expression
1		ineq1d.1	|- ( ph -> A = B )
2		ineq12d.2	|- ( ph -> C = D )
3		ineq12	|- ( ( A = B /\ C = D ) -> ( A i^i C ) = ( B i^i D ) )
4	1 2 3	syl2anc	|- ( ph -> ( A i^i C ) = ( B i^i D ) )