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Theorem bj-vecssmod 33690
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 19469 . 2 LVec = {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing}
2 ssrab2 3914 . 2 {𝑥 ∈ LMod ∣ (Scalar‘𝑥) ∈ DivRing} ⊆ LMod
31, 2eqsstri 3860 1 LVec ⊆ LMod
Colors of variables: wff setvar class
Syntax hints:  wcel 2164  {crab 3121  wss 3798  cfv 6127  Scalarcsca 16315  DivRingcdr 19110  LModclmod 19226  LVecclvec 19468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-rab 3126  df-in 3805  df-ss 3812  df-lvec 19469
This theorem is referenced by:  bj-vecssmodel  33691  bj-rrvecsscmn  33699
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