Theorem chex 5130

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

Assertion

Ref	Expression
chex	⊢ Cℋ ∈ V

Proof of Theorem chex

Step	Hyp	Ref	Expression
1		shex 5115	. 2 ⊢ Sℋ ∈ V
2		chsssh 5129	. 2 ⊢ Cℋ ⊆ Sℋ
3	1, 2	ssexi 1701	1 ⊢ Cℋ ∈ V

Syntax hints:   ∈ wcel 1092  Vcvv 1348   S_ℋ csh 4967   C_ℋ cch 4968

This theorem is referenced by:  stelt 5671

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-13 804  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075  ax-pow 1077  ax-hilex 4983

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-in 1491  df-ss 1492  df-pw 1799  df-sh 5114  df-ch 5127

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