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Mathbox for Stefan O'Rear |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > fglmod | Structured version Visualization version GIF version |
Description: Finitely generated left modules are left modules. (Contributed by Stefan O'Rear, 1-Jan-2015.) |
Ref | Expression |
---|---|
fglmod | β’ (π β LFinGen β π β LMod) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lfig 42492 | . . 3 β’ LFinGen = {π β LMod β£ (Baseβπ) β ((LSpanβπ) β (π« (Baseβπ) β© Fin))} | |
2 | 1 | ssrab3 4078 | . 2 β’ LFinGen β LMod |
3 | 2 | sseli 3976 | 1 β’ (π β LFinGen β π β LMod) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β wcel 2099 β© cin 3946 π« cpw 4603 β cima 5681 βcfv 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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