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Theorem nvclvec 18737
 Description: A normed vector space is a left vector space. (Contributed by Mario Carneiro, 4-Oct-2015.)
Assertion
Ref Expression
nvclvec NrmVec

Proof of Theorem nvclvec
StepHypRef Expression
1 isnvc 18735 . 2 NrmVec NrmMod
21simprbi 452 1 NrmVec
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1726  clvec 16179  NrmModcnlm 18633  NrmVeccnvc 18634 This theorem is referenced by:  nvctvc  18740  lssnvc  18742  sitgclbn  24662 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329  df-nvc 18640
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