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Theorem rellindf 27255
Description: The independent-family predicate is a proper relation and can be used with brrelexi 4918. (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 27253 . 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 5000 1  |-  Rel LIndF
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 359    e. wcel 1725   A.wral 2705   [.wsbc 3161    \ cdif 3317   {csn 3814   dom cdm 4878   "cima 4881   Rel wrel 4883   -->wf 5450   ` cfv 5454  (class class class)co 6081   Basecbs 13469  Scalarcsca 13532   .scvsca 13533   0gc0g 13723   LSpanclspn 16047   LIndF clindf 27251
This theorem is referenced by:  lindff  27262  lindfind  27263  f1lindf  27269  lindfmm  27274  lsslindf  27277
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-opab 4267  df-xp 4884  df-rel 4885  df-lindf 27253
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