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Theorem nvclvec 18309
Description: A normed vector space is a left vector space. (Contributed by Mario Carneiro, 4-Oct-2015.)
Assertion
Ref Expression
nvclvec  |-  ( W  e. NrmVec  ->  W  e.  LVec )

Proof of Theorem nvclvec
StepHypRef Expression
1 isnvc 18307 . 2  |-  ( W  e. NrmVec 
<->  ( W  e. NrmMod  /\  W  e.  LVec ) )
21simprbi 450 1  |-  ( W  e. NrmVec  ->  W  e.  LVec )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1710   LVecclvec 15954  NrmModcnlm 18205  NrmVeccnvc 18206
This theorem is referenced by:  nvctvc  18312  lssnvc  18314
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-v 2866  df-in 3235  df-nvc 18212
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