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Theorem rellindf 27381
Description: The independent-family predicate is a proper relation and can be used with brrelexi 4745. (Contributed by Stefan O'Rear, 24-Feb-2015.)
Assertion
Ref Expression
rellindf  |-  Rel LIndF

Proof of Theorem rellindf
Dummy variables  f 
k  s  w  x are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-lindf 27379 . 2  |- LIndF  =  { <. f ,  w >.  |  ( f : dom  f
--> ( Base `  w
)  /\  [. (Scalar `  w )  /  s ]. A. x  e.  dom  f A. k  e.  ( ( Base `  s
)  \  { ( 0g `  s ) } )  -.  ( k ( .s `  w
) ( f `  x ) )  e.  ( ( LSpan `  w
) `  ( f " ( dom  f  \  { x } ) ) ) ) }
21relopabi 4827 1  |-  Rel LIndF
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 358    e. wcel 1696   A.wral 2556   [.wsbc 3004    \ cdif 3162   {csn 3653   dom cdm 4705   "cima 4708   Rel wrel 4710   -->wf 5267   ` cfv 5271  (class class class)co 5874   Basecbs 13164  Scalarcsca 13227   .scvsca 13228   0gc0g 13416   LSpanclspn 15744   LIndF clindf 27377
This theorem is referenced by:  lindff  27388  lindfind  27389  f1lindf  27395  lindfmm  27400  lsslindf  27403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-opab 4094  df-xp 4711  df-rel 4712  df-lindf 27379
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