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Theorem fglmod 41429
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 41424 . . 3 LFinGen = {π‘Ž ∈ LMod ∣ (Baseβ€˜π‘Ž) ∈ ((LSpanβ€˜π‘Ž) β€œ (𝒫 (Baseβ€˜π‘Ž) ∩ Fin))}
21ssrab3 4045 . 2 LFinGen βŠ† LMod
32sseli 3945 1 (𝑀 ∈ LFinGen β†’ 𝑀 ∈ LMod)
Colors of variables: wff setvar class
Syntax hints:   β†’ wi 4   ∈ wcel 2107   ∩ cin 3914  π’« cpw 4565   β€œ cima 5641  β€˜cfv 6501  Fincfn 8890  Basecbs 17090  LModclmod 20338  LSpanclspn 20448  LFinGenclfig 41423
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3411  df-v 3450  df-in 3922  df-ss 3932  df-lfig 41424
This theorem is referenced by:  lnrfg  41475
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