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Theorem relwdom 7467
Description: Weak dominance is a relation. (Contributed by Stefan O'Rear, 11-Feb-2015.)
Assertion
Ref Expression
relwdom  |-  Rel  ~<_*

Proof of Theorem relwdom
Dummy variables  x  y  z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-wdom 7460 . 2  |-  ~<_*  =  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
21relopabi 4940 1  |-  Rel  ~<_*
Colors of variables: wff set class
Syntax hints:    \/ wo 358   E.wex 1547    = wceq 1649   (/)c0 3571   Rel wrel 4823   -onto->wfo 5392    ~<_* cwdom 7458
This theorem is referenced by:  brwdom  7468  brwdomi  7469  brwdomn0  7470  wdomtr  7476  wdompwdom  7479  canthwdom  7480  brwdom3i  7484  unwdomg  7485  xpwdomg  7486  wdomfil  7875  isfin32i  8178  hsmexlem1  8239  hsmexlem3  8241  wdomac  8338
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 2368  ax-sep 4271  ax-nul 4279  ax-pr 4344
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 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-ral 2654  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-opab 4208  df-xp 4824  df-rel 4825  df-wdom 7460
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