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Theorem chssii 22726
Description: A closed subspace of a Hilbert space is a subset of Hilbert space. (Contributed by NM, 6-Oct-1999.) (New usage is discouraged.)
Hypothesis
Ref Expression
chssi.1  |-  H  e. 
CH
Assertion
Ref Expression
chssii  |-  H  C_  ~H

Proof of Theorem chssii
StepHypRef Expression
1 chssi.1 . . 3  |-  H  e. 
CH
21chshii 22722 . 2  |-  H  e.  SH
32shssii 22707 1  |-  H  C_  ~H
Colors of variables: wff set class
Syntax hints:    e. wcel 1725    C_ wss 3312   ~Hchil 22414   CHcch 22424
This theorem is referenced by:  cheli  22727  chelii  22728  hhsscms  22771  chocvali  22793  chm1i  22950  chsscon3i  22955  chsscon2i  22957  chjoi  22982  chj1i  22983  shjshsi  22986  sshhococi  23040  h1dei  23044  spansnpji  23072  spanunsni  23073  h1datomi  23075  spansnji  23140  pjfi  23198  riesz3i  23557  hmopidmpji  23647  pjoccoi  23673  pjinvari  23686  stcltr2i  23770  mdsymi  23906  mdcompli  23924  dmdcompli  23925
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-hilex 22494
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-xp 4876  df-cnv 4878  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fv 5454  df-ov 6076  df-sh 22701  df-ch 22716
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