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Theorem fglmod 27171
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 27166 . . 3  |- LFinGen  =  {
a  e.  LMod  |  (
Base `  a )  e.  ( ( LSpan `  a
) " ( ~P ( Base `  a
)  i^i  Fin )
) }
2 ssrab2 3258 . . 3  |-  { a  e.  LMod  |  ( Base `  a )  e.  ( ( LSpan `  a
) " ( ~P ( Base `  a
)  i^i  Fin )
) }  C_  LMod
31, 2eqsstri 3208 . 2  |- LFinGen  C_  LMod
43sseli 3176 1  |-  ( M  e. LFinGen  ->  M  e.  LMod )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   {crab 2547    i^i cin 3151   ~Pcpw 3625   "cima 4692   ` cfv 5255   Fincfn 6863   Basecbs 13148   LModclmod 15627   LSpanclspn 15728  LFinGenclfig 27165
This theorem is referenced by:  lnrfg  27323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-in 3159  df-ss 3166  df-lfig 27166
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