Theorem alseu2d

Description: Deduction rule: Given "all some one" applied to a top-level inference, you can extract the "exactly one" part. (Contributed by David A. Wheeler, 21-Jul-2026)

	Ref	Expression
Hypothesis	alseu2d.1	|- ( ph -> AE! x ( ps -> ch ) )
Assertion	alseu2d	|- ( ph -> E! x ps )

Proof

Step	Hyp	Ref	Expression
1		alseu2d.1	|- ( ph -> AE! x ( ps -> ch ) )
2		df-alseu	|- ( 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	simprd	|- ( ph -> E! x ps )