Axiom ax-hcompl 24609

Description: Completeness of a Hilbert space. (Contributed by NM, 7-Aug-2000.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-hcompl	|- ( F e. Cauchy -> E. x e. ~H F ~~>v x )

Distinct variable group:   x, F

Detailed syntax breakdown of Axiom ax-hcompl

Step	Hyp	Ref	Expression
1		cF	. . 3 class F
2		ccau 24333	. . 3 class Cauchy
3	1, 2	wcel 1756	. 2 wff F e. Cauchy
4		vx	. . . . 5 setvar x
5	4	cv 1368	. . . 4 class x
6		chli 24334	. . . 4 class ~~>v
7	1, 5, 6	wbr 4297	. . 3 wff F ~~>v x
8		chil 24326	. . 3 class ~H
9	7, 4, 8	wrex 2721	. 2 wff E. x e. ~H F ~~>v x
10	3, 9	wi 4	1 wff ( F e. Cauchy -> E. x e. ~H F ~~>v x )

This axiom is referenced by:  hhcms  24610  isch3  24649  hhsscms  24685  occllem  24711  occl  24712  chscllem2  25046