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Mirrors > Home > MPE Home > Th. List > rellindf | Structured version Visualization version GIF version |
Description: The independent-family predicate is a proper relation and can be used with brrelexi 5297. (Contributed by Stefan O'Rear, 24-Feb-2015.) |
Ref | Expression |
---|---|
rellindf | ⊢ Rel LIndF |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lindf 20362 | . 2 ⊢ LIndF = {〈𝑓, 𝑤〉 ∣ (𝑓:dom 𝑓⟶(Base‘𝑤) ∧ [(Scalar‘𝑤) / 𝑠]∀𝑥 ∈ dom 𝑓∀𝑘 ∈ ((Base‘𝑠) ∖ {(0g‘𝑠)}) ¬ (𝑘( ·𝑠 ‘𝑤)(𝑓‘𝑥)) ∈ ((LSpan‘𝑤)‘(𝑓 “ (dom 𝑓 ∖ {𝑥}))))} | |
2 | 1 | relopabi 5383 | 1 ⊢ Rel LIndF |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∧ wa 382 ∈ wcel 2145 ∀wral 3061 [wsbc 3587 ∖ cdif 3720 {csn 4317 dom cdm 5250 “ cima 5253 Rel wrel 5255 ⟶wf 6026 ‘cfv 6030 (class class class)co 6796 Basecbs 16064 Scalarcsca 16152 ·𝑠 cvsca 16153 0gc0g 16308 LSpanclspn 19184 LIndF clindf 20360 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-9 2154 ax-10 2174 ax-11 2190 ax-12 2203 ax-13 2408 ax-ext 2751 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 837 df-3an 1073 df-tru 1634 df-ex 1853 df-nf 1858 df-sb 2050 df-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-rab 3070 df-v 3353 df-dif 3726 df-un 3728 df-in 3730 df-ss 3737 df-nul 4064 df-if 4227 df-sn 4318 df-pr 4320 df-op 4324 df-opab 4848 df-xp 5256 df-rel 5257 df-lindf 20362 |
This theorem is referenced by: lindff 20371 lindfind 20372 f1lindf 20378 lindfmm 20383 lsslindf 20386 |
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