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Theorem relwdom 9018
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 9017 . 2 * = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦onto𝑥)}
21relopabi 5671 1 Rel ≼*
Colors of variables: wff setvar class
Syntax hints:  wo 844   = wceq 1538  wex 1781  c0 4265  Rel wrel 5537  ontowfo 6332  * cwdom 9016
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-11 2161  ax-12 2178  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-un 3913  df-in 3915  df-ss 3925  df-sn 4540  df-pr 4542  df-op 4546  df-opab 5105  df-xp 5538  df-rel 5539  df-wdom 9017
This theorem is referenced by:  brwdom  9019  brwdomi  9020  brwdomn0  9021  wdomtr  9027  wdompwdom  9030  canthwdom  9031  brwdom3i  9035  unwdomg  9036  xpwdomg  9037  wdomfil  9476  isfin32i  9776  hsmexlem1  9837  hsmexlem3  9839  wdomac  9938
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