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Theorem relwdom 7526
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 7519 . 2  |-  ~<_*  =  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
21relopabi 4992 1  |-  Rel  ~<_*
Colors of variables: wff set class
Syntax hints:    \/ wo 358   E.wex 1550    = wceq 1652   (/)c0 3620   Rel wrel 4875   -onto->wfo 5444    ~<_* cwdom 7517
This theorem is referenced by:  brwdom  7527  brwdomi  7528  brwdomn0  7529  wdomtr  7535  wdompwdom  7538  canthwdom  7539  brwdom3i  7543  unwdomg  7544  xpwdomg  7545  wdomfil  7934  isfin32i  8237  hsmexlem1  8298  hsmexlem3  8300  wdomac  8397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259  df-xp 4876  df-rel 4877  df-wdom 7519
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