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Theorem relwdom 7296
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 7289 . 2  |-  ~<_*  =  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
21relopabi 4827 1  |-  Rel  ~<_*
Colors of variables: wff set class
Syntax hints:    \/ wo 357   E.wex 1531    = wceq 1632   (/)c0 3468   Rel wrel 4710   -onto->wfo 5269    ~<_* cwdom 7287
This theorem is referenced by:  brwdom  7297  brwdomi  7298  brwdomn0  7299  wdomtr  7305  wdompwdom  7308  canthwdom  7309  brwdom3i  7313  unwdomg  7314  xpwdomg  7315  wdomfil  7704  isfin32i  8007  hsmexlem1  8068  hsmexlem3  8070  wdomac  8168
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-opab 4094  df-xp 4711  df-rel 4712  df-wdom 7289
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