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Theorem refrel 26360
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 26346 . 2  |-  Ref  =  { <. x ,  y
>.  |  ( U. x  =  U. y  /\  A. z  e.  y  E. w  e.  x  z  C_  w ) }
21relopabi 5002 1  |-  Rel  Ref
Colors of variables: wff set class
Syntax hints:    /\ wa 360    = wceq 1653   A.wral 2707   E.wrex 2708    C_ wss 3322   U.cuni 4017   Rel wrel 4885   Refcref 26342
This theorem is referenced by:  isref  26361  refbas  26362  refssex  26363  reftr  26371  refssfne  26376
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-opab 4269  df-xp 4886  df-rel 4887  df-ref 26346
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