Theorem rspcdv

Description: Restricted specialization, using implicit substitution. (Contributed by NM, 17-Feb-2007) (Revised by Mario Carneiro, 4-Jan-2017)

	Ref	Expression
Hypotheses	rspcdv.1	|- ( ph -> A e. B )
	rspcdv.2	|- ( ( ph /\ x = A ) -> ( ps <-> ch ) )
Assertion	rspcdv	|- ( ph -> ( A. x e. B ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		rspcdv.1	|- ( ph -> A e. B )
2		rspcdv.2	|- ( ( ph /\ x = A ) -> ( ps <-> ch ) )
3	2	biimpd	|- ( ( ph /\ x = A ) -> ( ps -> ch ) )
4	1 3	rspcimdv	|- ( ph -> ( A. x e. B ps -> ch ) )