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Theorem fglmod 26833
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 26828 . . 3  |- LFinGen  =  {
a  e.  LMod  |  (
Base `  a )  e.  ( ( LSpan `  a
) " ( ~P ( Base `  a
)  i^i  Fin )
) }
2 ssrab2 3364 . . 3  |-  { a  e.  LMod  |  ( Base `  a )  e.  ( ( LSpan `  a
) " ( ~P ( Base `  a
)  i^i  Fin )
) }  C_  LMod
31, 2eqsstri 3314 . 2  |- LFinGen  C_  LMod
43sseli 3280 1  |-  ( M  e. LFinGen  ->  M  e.  LMod )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1717   {crab 2646    i^i cin 3255   ~Pcpw 3735   "cima 4814   ` cfv 5387   Fincfn 7038   Basecbs 13389   LModclmod 15870   LSpanclspn 15967  LFinGenclfig 26827
This theorem is referenced by:  lnrfg  26985
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-rab 2651  df-in 3263  df-ss 3270  df-lfig 26828
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