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Axiom ax-hcompl 28399
Description: Completeness of a Hilbert space. (Contributed by NM, 7-Aug-2000.) (New usage is discouraged.)
Assertion
Ref Expression
ax-hcompl (𝐹 ∈ Cauchy → ∃𝑥 ∈ ℋ 𝐹𝑣 𝑥)
Distinct variable group:   𝑥,𝐹

Detailed syntax breakdown of Axiom ax-hcompl
StepHypRef Expression
1 cF . . 3 class 𝐹
2 ccau 28123 . . 3 class Cauchy
31, 2wcel 2145 . 2 wff 𝐹 ∈ Cauchy
4 vx . . . . 5 setvar 𝑥
54cv 1630 . . . 4 class 𝑥
6 chli 28124 . . . 4 class 𝑣
71, 5, 6wbr 4786 . . 3 wff 𝐹𝑣 𝑥
8 chil 28116 . . 3 class
97, 4, 8wrex 3062 . 2 wff 𝑥 ∈ ℋ 𝐹𝑣 𝑥
103, 9wi 4 1 wff (𝐹 ∈ Cauchy → ∃𝑥 ∈ ℋ 𝐹𝑣 𝑥)
Colors of variables: wff setvar class
This axiom is referenced by:  hhcms  28400  isch3  28438  hhsscms  28476  occllem  28502  occl  28503  chscllem2  28837
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