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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 47210 | . 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 5819 | 1 β’ Rel linIndS |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β§ wa 394 = wceq 1539 β wcel 2104 βwral 3059 π« cpw 4601 class class class wbr 5147 Rel wrel 5680 βcfv 6542 (class class class)co 7411 βm cmap 8822 finSupp cfsupp 9363 Basecbs 17148 Scalarcsca 17204 0gc0g 17389 linC clinc 47172 linIndS clininds 47208 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-ext 2701 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1542 df-ex 1780 df-sb 2066 df-clab 2708 df-cleq 2722 df-clel 2808 df-v 3474 df-in 3954 df-ss 3964 df-opab 5210 df-xp 5681 df-rel 5682 df-lininds 47210 |
This theorem is referenced by: linindsv 47213 |
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