Theorem relwdom 9561

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 9560	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5821	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 846   = wceq 1542  ∃wex 1782  ∅c0 4323  Rel wrel 5682  –onto→wfo 6542   ≼^* cwdom 9559

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966  df-opab 5212  df-xp 5683  df-rel 5684  df-wdom 9560

This theorem is referenced by:  brwdom  9562  brwdomi  9563  brwdomn0  9564  wdomtr  9570  wdompwdom  9573  canthwdom  9574  brwdom3i  9578  unwdomg  9579  xpwdomg  9580  wdomfil  10056  isfin32i  10360  hsmexlem1  10421  hsmexlem3  10423  wdomac  10522