Theorem relwdom 9255

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 9254	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5719	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 843   = wceq 1539  ∃wex 1783  ∅c0 4253  Rel wrel 5585  –onto→wfo 6416   ≼^* cwdom 9253

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-opab 5133  df-xp 5586  df-rel 5587  df-wdom 9254

This theorem is referenced by:  brwdom  9256  brwdomi  9257  brwdomn0  9258  wdomtr  9264  wdompwdom  9267  canthwdom  9268  brwdom3i  9272  unwdomg  9273  xpwdomg  9274  wdomfil  9748  isfin32i  10052  hsmexlem1  10113  hsmexlem3  10115  wdomac  10214