Theorem exlimimdd

Description: Existential elimination rule of natural deduction. (Contributed by ML, 17-Jul-2020) Shorten exlimdd . (Revised by Wolf Lammen, 3-Sep-2023)

	Ref	Expression
Hypotheses	exlimdd.1	|- F/ x ph
	exlimdd.2	|- F/ x ch
	exlimdd.3	|- ( ph -> E. x ps )
	exlimimdd.4	|- ( ph -> ( ps -> ch ) )
Assertion	exlimimdd	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		exlimdd.1	|- F/ x ph
2		exlimdd.2	|- F/ x ch
3		exlimdd.3	|- ( ph -> E. x ps )
4		exlimimdd.4	|- ( ph -> ( ps -> ch ) )
5	1 2 4	exlimd	|- ( ph -> ( E. x ps -> ch ) )
6	3 5	mpd	|- ( ph -> ch )