Theorem alsc2d

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

	Ref	Expression
Hypothesis	alsc2d.1	|- ( ph -> A! x e. A ps )
Assertion	alsc2d	|- ( ph -> E. x x e. A )

Proof

Step	Hyp	Ref	Expression
1		alsc2d.1	|- ( ph -> A! x e. A ps )
2		df-alsc	|- ( A! x e. A ps <-> ( A. x e. A ps /\ E. x x e. A ) )
3	1 2	sylib	|- ( ph -> ( A. x e. A ps /\ E. x x e. A ) )
4	3	simprd	|- ( ph -> E. x x e. A )