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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rellininds | Structured version Visualization version GIF version |
Description: The class defining the relation between a module and its linearly independent subsets is a relation. (Contributed by AV, 13-Apr-2019.) |
Ref | Expression |
---|---|
rellininds | β’ Rel linIndS |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lininds 47211 | . 2 β’ linIndS = {β¨π , πβ© β£ (π β π« (Baseβπ) β§ βπ β ((Baseβ(Scalarβπ)) βm π )((π finSupp (0gβ(Scalarβπ)) β§ (π( linC βπ)π ) = (0gβπ)) β βπ₯ β π (πβπ₯) = (0gβ(Scalarβπ))))} | |
2 | 1 | relopabiv 5820 | 1 β’ Rel linIndS |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β§ wa 395 = wceq 1540 β wcel 2105 βwral 3060 π« cpw 4602 class class class wbr 5148 Rel wrel 5681 βcfv 6543 (class class class)co 7412 βm cmap 8824 finSupp cfsupp 9365 Basecbs 17149 Scalarcsca 17205 0gc0g 17390 linC clinc 47173 linIndS clininds 47209 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1543 df-ex 1781 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-v 3475 df-in 3955 df-ss 3965 df-opab 5211 df-xp 5682 df-rel 5683 df-lininds 47211 |
This theorem is referenced by: linindsv 47214 |
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