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Theorem relwdom 8456
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 8449 . 2 * = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦onto𝑥)}
21relopabi 5234 1 Rel ≼*
Colors of variables: wff setvar class
Syntax hints:  wo 383   = wceq 1481  wex 1702  c0 3907  Rel wrel 5109  ontowfo 5874  * cwdom 8447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-rab 2918  df-v 3197  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-if 4078  df-sn 4169  df-pr 4171  df-op 4175  df-opab 4704  df-xp 5110  df-rel 5111  df-wdom 8449
This theorem is referenced by:  brwdom  8457  brwdomi  8458  brwdomn0  8459  wdomtr  8465  wdompwdom  8468  canthwdom  8469  brwdom3i  8473  unwdomg  8474  xpwdomg  8475  wdomfil  8869  isfin32i  9172  hsmexlem1  9233  hsmexlem3  9235  wdomac  9334
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