Theorem ralseu2d

Description: Deduction rule: Given "all some one" applied to a class, you can extract the "exactly one" part. Note that the witness must satisfy the antecedent ps , not merely be a member of A . (Contributed by David A. Wheeler, 21-Jul-2026)

	Ref	Expression
Hypothesis	ralseu2d.1	|- ( ph -> AE! x e. A ( ps -> ch ) )
Assertion	ralseu2d	|- ( ph -> E! x e. A ps )

Proof

Step	Hyp	Ref	Expression
1		ralseu2d.1	|- ( ph -> AE! x e. A ( ps -> ch ) )
2		df-ralseu	|- ( AE! x e. A ( ps -> ch ) <-> ( A. x e. A ( ps -> ch ) /\ E! x e. A ps ) )
3	1 2	sylib	|- ( ph -> ( A. x e. A ( ps -> ch ) /\ E! x e. A ps ) )
4	3	simprd	|- ( ph -> E! x e. A ps )