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Theorem chex 24580
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 24565 . 2  |-  SH  e.  _V
2 chsssh 24579 . 2  |-  CH  C_  SH
31, 2ssexi 4432 1  |-  CH  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1756   _Vcvv 2967   SHcsh 24281   CHcch 24282
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419  ax-sep 4408  ax-pow 4465  ax-hilex 24352
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2716  df-rab 2719  df-v 2969  df-dif 3326  df-un 3328  df-in 3330  df-ss 3337  df-nul 3633  df-if 3787  df-pw 3857  df-sn 3873  df-pr 3875  df-op 3879  df-uni 4087  df-br 4288  df-opab 4346  df-xp 4841  df-cnv 4843  df-dm 4845  df-rn 4846  df-res 4847  df-ima 4848  df-iota 5376  df-fv 5421  df-ov 6089  df-sh 24560  df-ch 24575
This theorem is referenced by:  isst  25568  ishst  25569
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