Metamath Proof Explorer

Theorem isnvc

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

Ref Expression
Assertion isnvc 
|- ( W e. NrmVec <-> ( W e. NrmMod /\ W e. LVec ) )

Proof

Step Hyp Ref Expression
1 df-nvc 
 |-  NrmVec = ( NrmMod i^i LVec )
2 1 elin2 
 |-  ( W e. NrmVec <-> ( W e. NrmMod /\ W e. LVec ) )