Theorem relwdom 9458

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 9457	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5763	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 847   = wceq 1540  ∃wex 1779  ∅c0 4284  Rel wrel 5624  –onto→wfo 6480   ≼^* cwdom 9456

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3438  df-ss 3920  df-opab 5155  df-xp 5625  df-rel 5626  df-wdom 9457

This theorem is referenced by:  brwdom  9459  brwdomi  9460  brwdomn0  9461  wdomtr  9467  wdompwdom  9470  canthwdom  9471  brwdom3i  9475  unwdomg  9476  xpwdomg  9477  wdomfil  9955  isfin32i  10259  hsmexlem1  10320  hsmexlem3  10322  wdomac  10421