Mathbox for Stefan O'Rear < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  rellindf Structured version   Unicode version

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 LIndF

Proof of Theorem rellindf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-lindf 27253 . 2 LIndF Scalar
21relopabi 5000 1 LIndF
 Colors of variables: wff set class Syntax hints:   wn 3   wa 359   wcel 1725  wral 2705  wsbc 3161   cdif 3317  csn 3814   cdm 4878  cima 4881   wrel 4883  wf 5450  cfv 5454  (class class class)co 6081  cbs 13469  Scalarcsca 13532  cvsca 13533  c0g 13723  clspn 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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