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Theorem relwdom 9510
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 9509 . 2 * = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦onto𝑥)}
21relopabiv 5780 1 Rel ≼*
Colors of variables: wff setvar class
Syntax hints:  wo 846   = wceq 1542  wex 1782  c0 4286  Rel wrel 5642  ontowfo 6498  * cwdom 9508
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3449  df-in 3921  df-ss 3931  df-opab 5172  df-xp 5643  df-rel 5644  df-wdom 9509
This theorem is referenced by:  brwdom  9511  brwdomi  9512  brwdomn0  9513  wdomtr  9519  wdompwdom  9522  canthwdom  9523  brwdom3i  9527  unwdomg  9528  xpwdomg  9529  wdomfil  10005  isfin32i  10309  hsmexlem1  10370  hsmexlem3  10372  wdomac  10471
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