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Theorem relwdom 7895
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 7888 . 2  |-  ~<_*  =  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
21relopabi 5076 1  |-  Rel  ~<_*
Colors of variables: wff setvar class
Syntax hints:    \/ wo 368    = wceq 1370   E.wex 1587   (/)c0 3748   Rel wrel 4956   -onto->wfo 5527    ~<_* cwdom 7886
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pr 4642
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-if 3903  df-sn 3989  df-pr 3991  df-op 3995  df-opab 4462  df-xp 4957  df-rel 4958  df-wdom 7888
This theorem is referenced by:  brwdom  7896  brwdomi  7897  brwdomn0  7898  wdomtr  7904  wdompwdom  7907  canthwdom  7908  brwdom3i  7912  unwdomg  7913  xpwdomg  7914  wdomfil  8345  isfin32i  8648  hsmexlem1  8709  hsmexlem3  8711  wdomac  8808
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