Theorem relwdom 9473

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 9472	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5768	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 848   = wceq 1542  ∃wex 1781  ∅c0 4284  Rel wrel 5628  –onto→wfo 6489   ≼^* cwdom 9471

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 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2714  df-cleq 2727  df-clel 2810  df-v 3441  df-ss 3917  df-opab 5160  df-xp 5629  df-rel 5630  df-wdom 9472

This theorem is referenced by:  brwdom  9474  brwdomi  9475  brwdomn0  9476  wdomtr  9482  wdompwdom  9485  canthwdom  9486  brwdom3i  9490  unwdomg  9491  xpwdomg  9492  wdomfil  9973  isfin32i  10277  hsmexlem1  10338  hsmexlem3  10340  wdomac  10439