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Theorem relwdom 7280
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 7273 . 2  |-  ~<_*  =  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
21relopabi 4811 1  |-  Rel  ~<_*
Colors of variables: wff set class
Syntax hints:    \/ wo 357   E.wex 1528    = wceq 1623   (/)c0 3455   Rel wrel 4694   -onto->wfo 5253    ~<_* cwdom 7271
This theorem is referenced by:  brwdom  7281  brwdomi  7282  brwdomn0  7283  wdomtr  7289  wdompwdom  7292  canthwdom  7293  brwdom3i  7297  unwdomg  7298  xpwdomg  7299  wdomfil  7688  isfin32i  7991  hsmexlem1  8052  hsmexlem3  8054  wdomac  8152
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-wdom 7273
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