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Theorem fglmod 27274
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 27269 . . 3  |- LFinGen  =  {
a  e.  LMod  |  (
Base `  a )  e.  ( ( LSpan `  a
) " ( ~P ( Base `  a
)  i^i  Fin )
) }
2 ssrab2 3271 . . 3  |-  { a  e.  LMod  |  ( Base `  a )  e.  ( ( LSpan `  a
) " ( ~P ( Base `  a
)  i^i  Fin )
) }  C_  LMod
31, 2eqsstri 3221 . 2  |- LFinGen  C_  LMod
43sseli 3189 1  |-  ( M  e. LFinGen  ->  M  e.  LMod )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   {crab 2560    i^i cin 3164   ~Pcpw 3638   "cima 4708   ` cfv 5271   Fincfn 6879   Basecbs 13164   LModclmod 15643   LSpanclspn 15744  LFinGenclfig 27268
This theorem is referenced by:  lnrfg  27426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-in 3172  df-ss 3179  df-lfig 27269
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