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Theorem lveclmodd 20955
Description: A vector space is a left module. (Contributed by SN, 16-May-2024.)
Hypothesis
Ref Expression
lveclmodd.1 (𝜑𝑊 ∈ LVec)
Assertion
Ref Expression
lveclmodd (𝜑𝑊 ∈ LMod)

Proof of Theorem lveclmodd
StepHypRef Expression
1 lveclmodd.1 . 2 (𝜑𝑊 ∈ LVec)
2 lveclmod 20954 . 2 (𝑊 ∈ LVec → 𝑊 ∈ LMod)
31, 2syl 17 1 (𝜑𝑊 ∈ LMod)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  LModclmod 20706  LVecclvec 20950
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-iota 6489  df-fv 6545  df-lvec 20951
This theorem is referenced by:  lvecgrpd  20956  quslvec  32978  ply1degltdimlem  33225  algextdeglem8  33301  prjspner1  41946
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