MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  relwdom Structured version   Unicode version

Theorem relwdom 7995
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 7988 . 2  |-  ~<_*  =  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
21relopabi 5118 1  |-  Rel  ~<_*
Colors of variables: wff setvar class
Syntax hints:    \/ wo 368    = wceq 1383   E.wex 1599   (/)c0 3770   Rel wrel 4994   -onto->wfo 5576    ~<_* cwdom 7986
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-opab 4496  df-xp 4995  df-rel 4996  df-wdom 7988
This theorem is referenced by:  brwdom  7996  brwdomi  7997  brwdomn0  7998  wdomtr  8004  wdompwdom  8007  canthwdom  8008  brwdom3i  8012  unwdomg  8013  xpwdomg  8014  wdomfil  8445  isfin32i  8748  hsmexlem1  8809  hsmexlem3  8811  wdomac  8908
  Copyright terms: Public domain W3C validator