Axiom ax-hcompl 9056

Description: Completeness of a Hilbert space.

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 8780	. . 3 class Cauchy
3	1, 2	wcel 958	. 2 wff F e. Cauchy
4		vx	. . . . 5 set x
5	4	cv 955	. . . 4 class x
6		chli 8781	. . . 4 class ~~>v
7	1, 5, 6	wbr 2619	. . 3 wff F ~~>v x
8		chil 8773	. . 3 class H~
9	7, 4, 8	wrex 1646	. 2 wff E.x e. H~ F ~~>v x
10	3, 9	wi 3	1 wff (F e. Cauchy -> E.x e. H~ F ~~>v x)

This axiom is referenced by:  hhcms 9057  chsscm 9097

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