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Theorem fglmod 42497
Description: Finitely generated left modules are left modules. (Contributed by Stefan O'Rear, 1-Jan-2015.)
Assertion
Ref Expression
fglmod (𝑀 ∈ LFinGen β†’ 𝑀 ∈ LMod)

Proof of Theorem fglmod
StepHypRef Expression
1 df-lfig 42492 . . 3 LFinGen = {π‘Ž ∈ LMod ∣ (Baseβ€˜π‘Ž) ∈ ((LSpanβ€˜π‘Ž) β€œ (𝒫 (Baseβ€˜π‘Ž) ∩ Fin))}
21ssrab3 4078 . 2 LFinGen βŠ† LMod
32sseli 3976 1 (𝑀 ∈ LFinGen β†’ 𝑀 ∈ LMod)
Colors of variables: wff setvar class
Syntax hints:   β†’ wi 4   ∈ wcel 2099   ∩ cin 3946  π’« cpw 4603   β€œ cima 5681  β€˜cfv 6548  Fincfn 8964  Basecbs 17180  LModclmod 20743  LSpanclspn 20855  LFinGenclfig 42491
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3430  df-v 3473  df-in 3954  df-ss 3964  df-lfig 42492
This theorem is referenced by:  lnrfg  42543
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