Theorem relwdom 9541

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 9540	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5805	1 ⊢ Rel ≼*

This proof depends on syntax axioms:   ∨ wo 861   = wceq 1570  ∃wex 1812  ∅c0 4282  Rel wrel 5664  –onto→wfo 6535   ≼^* cwdom 9539

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3455  df-ss 3919  df-opab 5172  df-xp 5665  df-rel 5666  df-wdom 9540

This theorem is used by:  brwdom  9542  brwdomi  9543  brwdomn0  9544  wdomtr  9550  wdompwdom  9553  canthwdom  9554  brwdom3i  9558  unwdomg  9559  xpwdomg  9560  wdomfil  10067  isfin32i  10370  hsmexlem1  10431  hsmexlem3  10433  wdomac  10533