Axiom ax-hcompl 9073

Description: Completeness of a Hilbert space.

Assertion

Ref	Expression
ax-hcompl	⊢ (F ∈ Cauchy → ∃x ∈ 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 8797	. . 3 class Cauchy
3	1, 2	wcel 960	. 2 wff F ∈ Cauchy
4		vx	. . . . 5 set x
5	4	cv 957	. . . 4 class x
6		chli 8798	. . . 4 class ⇝v
7	1, 5, 6	wbr 2625	. . 3 wff F ⇝v x
8		chil 8790	. . 3 class ℋ
9	7, 4, 8	wrex 1649	. 2 wff ∃x ∈ ℋ F ⇝v x
10	3, 9	wi 3	1 wff (F ∈ Cauchy → ∃x ∈ ℋ F ⇝v x)

This axiom is referenced by:  hhcms 9074  chsscm 9114

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