Axiom ax-hcompl 5113

Description: Completeness of a Hilbert space.

Assertion

Ref	Expression
ax-hcompl	⊢ (F ∈ Cauchy → ∃x ∈ ℋ F ⇝v x)

Distinct variable group(s):   x,F

Detailed syntax breakdown of Axiom ax-hcompl

Step	Hyp	Ref	Expression
1		cF	. . 3 class F
2		ccau 4965	. . 3 class Cauchy
3	1, 2	wcel 1092	. 2 wff F ∈ Cauchy
4		vx	. . . . 5 set x
5	4	cv 1089	. . . 4 class x
6		chli 4966	. . . 4 class ⇝v
7	1, 5, 6	wbr 2054	. . 3 wff F ⇝v x
8		chil 4958	. . 3 class ℋ
9	7, 4, 8	wrex 1202	. 2 wff ∃x ∈ ℋ F ⇝v x
10	3, 9	wi 2	1 wff (F ∈ Cauchy → ∃x ∈ ℋ F ⇝v x)

This axiom is referenced by:  chsscm 5147

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