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Theorem lvecgrp 39383
 Description: A vector space is a group. (Contributed by SN, 28-May-2023.)
Assertion
Ref Expression
lvecgrp (𝑊 ∈ LVec → 𝑊 ∈ Grp)

Proof of Theorem lvecgrp
StepHypRef Expression
1 lveclmod 19881 . 2 (𝑊 ∈ LVec → 𝑊 ∈ LMod)
2 lmodgrp 19644 . 2 (𝑊 ∈ LMod → 𝑊 ∈ Grp)
31, 2syl 17 1 (𝑊 ∈ LVec → 𝑊 ∈ Grp)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2115  Grpcgrp 18106  LModclmod 19637  LVecclvec 19877 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-nul 5197 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-rab 3142  df-v 3483  df-sbc 3760  df-dif 3923  df-un 3925  df-in 3927  df-ss 3937  df-nul 4278  df-sn 4552  df-pr 4554  df-op 4558  df-uni 4826  df-br 5054  df-iota 6303  df-fv 6352  df-ov 7153  df-lmod 19639  df-lvec 19878 This theorem is referenced by: (None)
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