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Theorem bj-vecssmod 31443
Description: Vector spaces are modules. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-vecssmod  |-  LVec  C_  LMod

Proof of Theorem bj-vecssmod
StepHypRef Expression
1 df-lvec 18261 . 2  |-  LVec  =  { x  e.  LMod  |  (Scalar `  x )  e.  DivRing }
2 ssrab2 3552 . 2  |-  { x  e.  LMod  |  (Scalar `  x )  e.  DivRing } 
C_  LMod
31, 2eqsstri 3500 1  |-  LVec  C_  LMod
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1870   {crab 2786    C_ wss 3442   ` cfv 5601  Scalarcsca 15155   DivRingcdr 17910   LModclmod 18026   LVecclvec 18260
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rab 2791  df-in 3449  df-ss 3456  df-lvec 18261
This theorem is referenced by:  bj-vecssmodel  31444  bj-rrvecsscmn  31452
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