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Metamath Proof Explorer

Theorem chex

Description: The set of closed subspaces of a Hilbert space exists (is a set). (Contributed by NM, 23-Oct-1999) (New usage is discouraged.)

Ref Expression
Assertion chex ⊢ C ℋ ∈ V

Proof

Step Hyp Ref Expression
1 shex ⊢ S ℋ ∈ V
2 chsssh ⊢ C ℋ ⊆ S ℋ
3 1 2 ssexi ⊢ C ℋ ∈ V