Theorem relwdom 9563

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 9562	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5820	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 845   = wceq 1541  ∃wex 1781  ∅c0 4322  Rel wrel 5681  –onto→wfo 6541   ≼^* cwdom 9561

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-in 3955  df-ss 3965  df-opab 5211  df-xp 5682  df-rel 5683  df-wdom 9562

This theorem is referenced by:  brwdom  9564  brwdomi  9565  brwdomn0  9566  wdomtr  9572  wdompwdom  9575  canthwdom  9576  brwdom3i  9580  unwdomg  9581  xpwdomg  9582  wdomfil  10058  isfin32i  10362  hsmexlem1  10423  hsmexlem3  10425  wdomac  10524