Theorem relwdom 9635

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 9634	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5844	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 846   = wceq 1537  ∃wex 1777  ∅c0 4352  Rel wrel 5705  –onto→wfo 6571   ≼^* cwdom 9633

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-ss 3993  df-opab 5229  df-xp 5706  df-rel 5707  df-wdom 9634

This theorem is referenced by:  brwdom  9636  brwdomi  9637  brwdomn0  9638  wdomtr  9644  wdompwdom  9647  canthwdom  9648  brwdom3i  9652  unwdomg  9653  xpwdomg  9654  wdomfil  10130  isfin32i  10434  hsmexlem1  10495  hsmexlem3  10497  wdomac  10596