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Theorem bj-vecssmod 36100
Description: Vector spaces are modules. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-vecssmod LVec ⊆ LMod

Proof of Theorem bj-vecssmod
StepHypRef Expression
1 df-lvec 20702 . 2 LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing}
2 ssrab2 4076 . 2 {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod
31, 2eqsstri 4015 1 LVec ⊆ LMod
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  {crab 3433  wss 3947  cfv 6540  Scalarcsca 17196  DivRingcdr 20304  LModclmod 20459  LVecclvec 20701
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 3954  df-ss 3964  df-lvec 20702
This theorem is referenced by:  bj-vecssmodel  36101
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