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Theorem bj-vecssmodel 36163
Description: Vector spaces are modules (elemental version). This is a shorter proof of lveclmod 20717. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-vecssmodel (𝐴 ∈ LVec → 𝐴 ∈ LMod)

Proof of Theorem bj-vecssmodel
StepHypRef Expression
1 bj-vecssmod 36162 . 2 LVec ⊆ LMod
21sseli 3979 1 (𝐴 ∈ LVec → 𝐴 ∈ LMod)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  LModclmod 20471  LVecclvec 20713
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-in 3956  df-ss 3966  df-lvec 20714
This theorem is referenced by:  bj-isrvec2  36181
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