Theorem relwdom 9475

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 9474	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5766	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 854   = wceq 1548  ∃wex 1787  ∅c0 4264  Rel wrel 5626  –onto→wfo 6487   ≼^* cwdom 9473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-ext 2713

This theorem depends on definitions:  df-bi 209  df-an 398  df-tru 1551  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-v 3435  df-ss 3902  df-opab 5138  df-xp 5627  df-rel 5628  df-wdom 9474

This theorem is referenced by:  brwdom  9476  brwdomi  9477  brwdomn0  9478  wdomtr  9484  wdompwdom  9487  canthwdom  9488  brwdom3i  9492  unwdomg  9493  xpwdomg  9494  wdomfil  9978  isfin32i  10282  hsmexlem1  10343  hsmexlem3  10345  wdomac  10444