Axiom ax-hcompl 11540

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 11265	. . 3 class Cauchy
3	1, 2	wcel 1588	. 2 wff F e. Cauchy
4		vx	. . . . 5 set x
5	4	cv 1585	. . . 4 class x
6		chli 11266	. . . 4 class ~~>v
7	1, 5, 6	wbr 3507	. . 3 wff F ~~>v x
8		chil 11258	. . 3 class ~H
9	7, 4, 8	wrex 2356	. 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 11541  chsscmi 11579

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