Metamath Proof Explorer

Theorem nvclvec

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

Ref Expression
Assertion nvclvec 
|- ( W e. NrmVec -> W e. LVec )

Proof

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