Theorem spcdv

Description: Rule of specialization, using implicit substitution. Analogous to rspcdv . (Contributed by David Moews, 1-May-2017)

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

Proof

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