Theorem relwdom 9606

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 9605	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5830	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 848   = wceq 1540  ∃wex 1779  ∅c0 4333  Rel wrel 5690  –onto→wfo 6559   ≼^* cwdom 9604

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-ss 3968  df-opab 5206  df-xp 5691  df-rel 5692  df-wdom 9605

This theorem is referenced by:  brwdom  9607  brwdomi  9608  brwdomn0  9609  wdomtr  9615  wdompwdom  9618  canthwdom  9619  brwdom3i  9623  unwdomg  9624  xpwdomg  9625  wdomfil  10101  isfin32i  10405  hsmexlem1  10466  hsmexlem3  10468  wdomac  10567