Theorem chex 9095

Description: The set of closed subspaces of a Hilbert space exists (is a set).

Assertion

Ref	Expression
chex	|- CH e. V

Proof of Theorem chex

Step	Hyp	Ref	Expression
1		shex 9077	. 2 |- SH e. V
2		chsssh 9094	. 2 |- CH (_ SH
3	1, 2	ssexi 2720	1 |- CH e. V

Syntax hints:   e. wcel 958  Vcvv 1811  SHcsh 8797  CHcch 8798

This theorem is referenced by:  stelt 10141  hstelt 10142

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-13 969  ax-14 970  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459  ax-sep 2703  ax-pow 2742  ax-hilex 8869

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-in 2051  df-ss 2053  df-pw 2402  df-sh 9076  df-ch 9092

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