Theorem als1d

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

	Ref	Expression
Hypothesis	als1d.1	|- ( ph -> AE x ( ps -> ch ) )
Assertion	als1d	|- ( ph -> A. x ( ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		als1d.1	|- ( ph -> AE x ( ps -> ch ) )
2		df-als	|- ( AE x ( ps -> ch ) <-> ( A. x ( ps -> ch ) /\ E. x ps ) )
3	1 2	sylib	|- ( ph -> ( A. x ( ps -> ch ) /\ E. x ps ) )
4	3	simpld	|- ( ph -> A. x ( ps -> ch ) )