Theorem relwdom 9485

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 9484	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5779	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 848   = wceq 1542  ∃wex 1781  ∅c0 4287  Rel wrel 5639  –onto→wfo 6500   ≼^* cwdom 9483

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 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3444  df-ss 3920  df-opab 5163  df-xp 5640  df-rel 5641  df-wdom 9484

This theorem is referenced by:  brwdom  9486  brwdomi  9487  brwdomn0  9488  wdomtr  9494  wdompwdom  9497  canthwdom  9498  brwdom3i  9502  unwdomg  9503  xpwdomg  9504  wdomfil  9985  isfin32i  10289  hsmexlem1  10350  hsmexlem3  10352  wdomac  10451