Metamath Proof Explorer


Theorem chsssh

Description: Closed subspaces are subspaces in a Hilbert space. (Contributed by NM, 29-May-1999) (Revised by Mario Carneiro, 23-Dec-2013) (New usage is discouraged.)

Ref Expression
Assertion chsssh
|- CH C_ SH

Proof

Step Hyp Ref Expression
1 chsh
 |-  ( x e. CH -> x e. SH )
2 1 ssriv
 |-  CH C_ SH