Theorem nfralseu

Description: Bound-variable hypothesis builder for "all some one" restricted to a class. This is the "all some one" counterpart of nfrals . (Contributed by David A. Wheeler, 21-Jul-2026)

	Ref	Expression
Hypotheses	nfralseu.1	|- F/_ x A
	nfralseu.2	|- F/ x ph
	nfralseu.3	|- F/ x ps
Assertion	nfralseu	|- F/ x AE! y e. A ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		nfralseu.1	|- F/_ x A
2		nfralseu.2	|- F/ x ph
3		nfralseu.3	|- F/ x ps
4		df-ralseu	|- ( AE! y e. A ( ph -> ps ) <-> ( A. y e. A ( ph -> ps ) /\ E! y e. A ph ) )
5	2 3	nfim	|- F/ x ( ph -> ps )
6	1 5	nfralw	|- F/ x A. y e. A ( ph -> ps )
7	1 2	nfreuw	|- F/ x E! y e. A ph
8	6 7	nfan	|- F/ x ( A. y e. A ( ph -> ps ) /\ E! y e. A ph )
9	4 8	nfxfr	|- F/ x AE! y e. A ( ph -> ps )