Metamath Proof Explorer

Theorem chss

Description: A closed subspace of a Hilbert space is a subset of Hilbert space. (Contributed by NM, 24-Aug-1999) (New usage is discouraged.)

Ref Expression
Assertion chss 
|- ( H e. CH -> H C_ ~H )

Proof

Step Hyp Ref Expression
1 chsh 
 |-  ( H e. CH -> H e. SH )
2 shss 
 |-  ( H e. SH -> H C_ ~H )
3 1 2 syl 
 |-  ( H e. CH -> H C_ ~H )