Metamath Proof Explorer

Theorem chssii

Description: A closed subspace of a Hilbert space is a subset of Hilbert space. (Contributed by NM, 6-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypothesis chssi.1 
|- H e. CH
Assertion chssii 
|- H C_ ~H

Proof

Step Hyp Ref Expression
1 chssi.1 
 |-  H e. CH
2 1 chshii 
 |-  H e. SH
3 2 shssii 
 |-  H C_ ~H