Theorem exlimimd

Description: Existential elimination rule of natural deduction. (Contributed by ML, 17-Jul-2020)

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

Proof

Step	Hyp	Ref	Expression
1		exlimimd.1	|- ( ph -> E. x ps )
2		exlimimd.2	|- ( ph -> ( ps -> ch ) )
3	2	imp	|- ( ( ph /\ ps ) -> ch )
4	1 3	exlimddv	|- ( ph -> ch )