Theorem exlimddv

Description: Existential elimination rule of natural deduction (Rule C, explained in exlimiv ). (Contributed by Mario Carneiro, 15-Jun-2016)

	Ref	Expression
Hypotheses	exlimddv.1	|- ( ph -> E. x ps )
	exlimddv.2	|- ( ( ph /\ ps ) -> ch )
Assertion	exlimddv	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		exlimddv.1	|- ( ph -> E. x ps )
2		exlimddv.2	|- ( ( ph /\ ps ) -> ch )
3	2	ex	|- ( ph -> ( ps -> ch ) )
4	3	exlimdv	|- ( ph -> ( E. x ps -> ch ) )
5	1 4	mpd	|- ( ph -> ch )