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Theorem relwdom 8354
 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 8347 . 2 * = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦onto𝑥)}
21relopabi 5167 1 Rel ≼*
 Colors of variables: wff setvar class Syntax hints:   ∨ wo 382   = wceq 1475  ∃wex 1695  ∅c0 3874  Rel wrel 5043  –onto→wfo 5802   ≼* cwdom 8345 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-opab 4644  df-xp 5044  df-rel 5045  df-wdom 8347 This theorem is referenced by:  brwdom  8355  brwdomi  8356  brwdomn0  8357  wdomtr  8363  wdompwdom  8366  canthwdom  8367  brwdom3i  8371  unwdomg  8372  xpwdomg  8373  wdomfil  8767  isfin32i  9070  hsmexlem1  9131  hsmexlem3  9133  wdomac  9230
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