Theorem rexlimddv

Description: Restricted existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 15-Jun-2016)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimddv.1	|- ( ph -> E. x e. A ps )
2		rexlimddv.2	|- ( ( ph /\ ( x e. A /\ ps ) ) -> ch )
3	2	rexlimdvaa	|- ( ph -> ( E. x e. A ps -> ch ) )
4	1 3	mpd	|- ( ph -> ch )