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Theorem bj-vecssmod 34599
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 19861 . 2 LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing}
2 ssrab2 4040 . 2 {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod
31, 2eqsstri 3985 1 LVec ⊆ LMod
Colors of variables: wff setvar class
Syntax hints:  wcel 2115  {crab 3136  wss 3918  cfv 6336  Scalarcsca 16557  DivRingcdr 19488  LModclmod 19620  LVecclvec 19860
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
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-rab 3141  df-v 3481  df-in 3925  df-ss 3935  df-lvec 19861
This theorem is referenced by:  bj-vecssmodel  34600
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