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Theorem bj-vecssmod 33740
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 17544 . 2  |-  LVec  =  { x  e.  LMod  |  (Scalar `  x )  e.  DivRing }
2 ssrab2 3585 . 2  |-  { x  e.  LMod  |  (Scalar `  x )  e.  DivRing } 
C_  LMod
31, 2eqsstri 3534 1  |-  LVec  C_  LMod
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1767   {crab 2818    C_ wss 3476   ` cfv 5587  Scalarcsca 14557   DivRingcdr 17191   LModclmod 17307   LVecclvec 17543
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2823  df-in 3483  df-ss 3490  df-lvec 17544
This theorem is referenced by:  bj-vecssmodel  33741  bj-rrvecsscmn  33749
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