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Theorem bj-vecssmodel 31645
Description: Vector spaces are modules (elemental version). This is a shorter proof of lveclmod 18307. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-vecssmodel  |-  ( A  e.  LVec  ->  A  e. 
LMod )

Proof of Theorem bj-vecssmodel
StepHypRef Expression
1 bj-vecssmod 31644 . 2  |-  LVec  C_  LMod
21sseli 3457 1  |-  ( A  e.  LVec  ->  A  e. 
LMod )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1867   LModclmod 18069   LVecclvec 18303
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 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398
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 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-rab 2782  df-in 3440  df-ss 3447  df-lvec 18304
This theorem is referenced by: (None)
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