Metamath Proof Explorer

Theorem nvcnlm

Description: A normed vector space is a normed module. (Contributed by Mario Carneiro, 4-Oct-2015)

Ref Expression
Assertion nvcnlm 
|- ( W e. NrmVec -> W e. NrmMod )

Proof

Step Hyp Ref Expression
1 isnvc 
 |-  ( W e. NrmVec <-> ( W e. NrmMod /\ W e. LVec ) )
2 1 simplbi 
 |-  ( W e. NrmVec -> W e. NrmMod )