Theorem relwdom 9014

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.

Step	Hyp	Ref	Expression
1		df-wdom 9013	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabi 5658	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 844   = wceq 1538  ∃wex 1781  ∅c0 4243  Rel wrel 5524  –onto→wfo 6322   ≼^* cwdom 9012

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 2113  ax-9 2121  ax-11 2158  ax-12 2175  ax-ext 2770

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 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-sn 4526  df-pr 4528  df-op 4532  df-opab 5093  df-xp 5525  df-rel 5526  df-wdom 9013

This theorem is referenced by:  brwdom  9015  brwdomi  9016  brwdomn0  9017  wdomtr  9023  wdompwdom  9026  canthwdom  9027  brwdom3i  9031  unwdomg  9032  xpwdomg  9033  wdomfil  9472  isfin32i  9776  hsmexlem1  9837  hsmexlem3  9839  wdomac  9938