Theorem relwdom 9481

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 9480	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5776	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 848   = wceq 1542  ∃wex 1781  ∅c0 4273  Rel wrel 5636  –onto→wfo 6496   ≼^* cwdom 9479

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431  df-ss 3906  df-opab 5148  df-xp 5637  df-rel 5638  df-wdom 9480

This theorem is referenced by:  brwdom  9482  brwdomi  9483  brwdomn0  9484  wdomtr  9490  wdompwdom  9493  canthwdom  9494  brwdom3i  9498  unwdomg  9499  xpwdomg  9500  wdomfil  9983  isfin32i  10287  hsmexlem1  10348  hsmexlem3  10350  wdomac  10449