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Theorem fglmod 27103
Description: Finitely generated left modules are left modules. (Contributed by Stefan O'Rear, 1-Jan-2015.)
Assertion
Ref Expression
fglmod  |-  ( M  e. LFinGen  ->  M  e.  LMod )

Proof of Theorem fglmod
StepHypRef Expression
1 df-lfig 27098 . . 3  |- LFinGen  =  {
a  e.  LMod  |  (
Base `  a )  e.  ( ( LSpan `  a
) " ( ~P ( Base `  a
)  i^i  Fin )
) }
2 ssrab2 3420 . . 3  |-  { a  e.  LMod  |  ( Base `  a )  e.  ( ( LSpan `  a
) " ( ~P ( Base `  a
)  i^i  Fin )
) }  C_  LMod
31, 2eqsstri 3370 . 2  |- LFinGen  C_  LMod
43sseli 3336 1  |-  ( M  e. LFinGen  ->  M  e.  LMod )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   {crab 2701    i^i cin 3311   ~Pcpw 3791   "cima 4873   ` cfv 5446   Fincfn 7101   Basecbs 13459   LModclmod 15940   LSpanclspn 16037  LFinGenclfig 27097
This theorem is referenced by:  lnrfg  27255
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-in 3319  df-ss 3326  df-lfig 27098
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