Theorem alsi2d

Description: Deduction rule: Given "all some" applied to a top-level inference, you can extract the "exists" part. (Contributed by David A. Wheeler, 20-Oct-2018)

	Ref	Expression
Hypothesis	alsi2d.1	|- ( ph -> A! x ( ps -> ch ) )
Assertion	alsi2d	|- ( ph -> E. x ps )

Proof

Step	Hyp	Ref	Expression
1		alsi2d.1	|- ( ph -> A! x ( ps -> ch ) )
2		df-alsi	|- ( A! x ( ps -> ch ) <-> ( A. x ( ps -> ch ) /\ E. x ps ) )
3	1 2	sylib	|- ( ph -> ( A. x ( ps -> ch ) /\ E. x ps ) )
4	3	simprd	|- ( ph -> E. x ps )