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Theorem rellindf 27278
Description: The independent-family predicate is a proper relation and can be used with brrelexi 4729. (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 27276 . 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 4811 1  |-  Rel LIndF
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 358    e. wcel 1684   A.wral 2543   [.wsbc 2991    \ cdif 3149   {csn 3640   dom cdm 4689   "cima 4692   Rel wrel 4694   -->wf 5251   ` cfv 5255  (class class class)co 5858   Basecbs 13148  Scalarcsca 13211   .scvsca 13212   0gc0g 13400   LSpanclspn 15728   LIndF clindf 27274
This theorem is referenced by:  lindff  27285  lindfind  27286  f1lindf  27292  lindfmm  27297  lsslindf  27300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-xp 4695  df-rel 4696  df-lindf 27276
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