Metamath Proof Explorer

Theorem hlbn

Description: Every subcomplex Hilbert space is a Banach space. (Contributed by Steve Rodriguez, 28-Apr-2007)

Ref Expression
Assertion hlbn 
|- ( W e. CHil -> W e. Ban )

Proof

Step Hyp Ref Expression
1 ishl 
 |-  ( W e. CHil <-> ( W e. Ban /\ W e. CPreHil ) )
2 1 simplbi 
 |-  ( W e. CHil -> W e. Ban )