Theorem relwdom 9603

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 9602	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5832	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 847   = wceq 1536  ∃wex 1775  ∅c0 4338  Rel wrel 5693  –onto→wfo 6560   ≼^* cwdom 9601

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-ss 3979  df-opab 5210  df-xp 5694  df-rel 5695  df-wdom 9602

This theorem is referenced by:  brwdom  9604  brwdomi  9605  brwdomn0  9606  wdomtr  9612  wdompwdom  9615  canthwdom  9616  brwdom3i  9620  unwdomg  9621  xpwdomg  9622  wdomfil  10098  isfin32i  10402  hsmexlem1  10463  hsmexlem3  10465  wdomac  10564