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Theorem chex 26271
Description: The set of closed subspaces of a Hilbert space exists (is a set). (Contributed by NM, 23-Oct-1999.) (New usage is discouraged.)
Assertion
Ref Expression
chex  |-  CH  e.  _V

Proof of Theorem chex
StepHypRef Expression
1 shex 26256 . 2  |-  SH  e.  _V
2 chsssh 26270 . 2  |-  CH  C_  SH
31, 2ssexi 4601 1  |-  CH  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1819   _Vcvv 3109   SHcsh 25972   CHcch 25973
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-pow 4634  ax-hilex 26043
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-pw 4017  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-opab 4516  df-xp 5014  df-cnv 5016  df-dm 5018  df-rn 5019  df-res 5020  df-ima 5021  df-iota 5557  df-fv 5602  df-ov 6299  df-sh 26251  df-ch 26266
This theorem is referenced by:  isst  27259  ishst  27260
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