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Theorem refrel 26278
Description: Refinement is a relation. (Contributed by Jeff Hankins, 18-Jan-2010.)
Assertion
Ref Expression
refrel  |-  Rel  Ref

Proof of Theorem refrel
Dummy variables  x  w  y  z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ref 26264 . 2  |-  Ref  =  { <. x ,  y
>.  |  ( U. x  =  U. y  /\  A. z  e.  y  E. w  e.  x  z  C_  w ) }
21relopabi 4811 1  |-  Rel  Ref
Colors of variables: wff set class
Syntax hints:    /\ wa 358    = wceq 1623   A.wral 2543   E.wrex 2544    C_ wss 3152   U.cuni 3827   Rel wrel 4694   Refcref 26260
This theorem is referenced by:  isref  26279  refbas  26280  refssex  26281  reftr  26289  refssfne  26294
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-ref 26264
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