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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 41424 | . . 3 β’ LFinGen = {π β LMod β£ (Baseβπ) β ((LSpanβπ) β (π« (Baseβπ) β© Fin))} | |
2 | 1 | ssrab3 4045 | . 2 β’ LFinGen β LMod |
3 | 2 | sseli 3945 | 1 β’ (π β LFinGen β π β LMod) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β wcel 2107 β© cin 3914 π« cpw 4565 β cima 5641 βcfv 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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