Metamath Proof Explorer

Theorem nvclmod

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

Ref Expression
Assertion nvclmod 
|- ( W e. NrmVec -> W e. LMod )

Proof

Step Hyp Ref Expression
1 nvcnlm 
 |-  ( W e. NrmVec -> W e. NrmMod )
2 nlmlmod 
 |-  ( W e. NrmMod -> W e. LMod )
3 1 2 syl 
 |-  ( W e. NrmVec -> W e. LMod )