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Axiom ax-hcompl 26690
Description: Completeness of a Hilbert space. (Contributed by NM, 7-Aug-2000.) (New usage is discouraged.)
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
StepHypRef Expression
1 cF . . 3  class  F
2 ccau 26414 . . 3  class  Cauchy
31, 2wcel 1870 . 2  wff  F  e. 
Cauchy
4 vx . . . . 5  setvar  x
54cv 1436 . . . 4  class  x
6 chli 26415 . . . 4  class  ~~>v
71, 5, 6wbr 4426 . . 3  wff  F  ~~>v  x
8 chil 26407 . . 3  class  ~H
97, 4, 8wrex 2783 . 2  wff  E. x  e.  ~H  F  ~~>v  x
103, 9wi 4 1  wff  ( F  e.  Cauchy  ->  E. x  e.  ~H  F  ~~>v  x )
Colors of variables: wff setvar class
This axiom is referenced by:  hhcms  26691  isch3  26729  hhsscms  26765  occllem  26791  occl  26792  chscllem2  27126
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