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Theorem fnerel 26040
Description: Fineness is a relation. (Contributed by Jeff Hankins, 28-Sep-2009.)
Assertion
Ref Expression
fnerel  |-  Rel  Fne

Proof of Theorem fnerel
Dummy variables  x  y  z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-fne 26036 . 2  |-  Fne  =  { <. x ,  y
>.  |  ( U. x  =  U. y  /\  A. z  e.  x  z  C_  U. ( y  i^i  ~P z ) ) }
21relopabi 4942 1  |-  Rel  Fne
Colors of variables: wff set class
Syntax hints:    /\ wa 359    = wceq 1649   A.wral 2651    i^i cin 3264    C_ wss 3265   ~Pcpw 3744   U.cuni 3959   Rel wrel 4825   Fnecfne 26032
This theorem is referenced by:  isfne  26041  isfne4  26042  fnetr  26059  fneval  26060  fneer  26061  fnessref  26066
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-sep 4273  ax-nul 4281  ax-pr 4346
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-ral 2656  df-rex 2657  df-rab 2660  df-v 2903  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-op 3768  df-opab 4210  df-xp 4826  df-rel 4827  df-fne 26036
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