Metamath Proof Explorer

Theorem hlcms

Description: Every subcomplex Hilbert space is a complete metric space. (Contributed by Mario Carneiro, 17-Oct-2015)

Ref Expression
Assertion hlcms 
|- ( W e. CHil -> W e. CMetSp )

Proof

Step Hyp Ref Expression
1 hlbn 
 |-  ( W e. CHil -> W e. Ban )
2 bncms 
 |-  ( W e. Ban -> W e. CMetSp )
3 1 2 syl 
 |-  ( W e. CHil -> W e. CMetSp )