Theorem relwdom 9516

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 9515	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5795	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 858   = wceq 1562  ∃wex 1801  ∅c0 4287  Rel wrel 5654  –onto→wfo 6521   ≼^* cwdom 9514

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1565  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-v 3458  df-ss 3923  df-opab 5165  df-xp 5655  df-rel 5656  df-wdom 9515

This theorem is referenced by:  brwdom  9517  brwdomi  9518  brwdomn0  9519  wdomtr  9525  wdompwdom  9528  canthwdom  9529  brwdom3i  9533  unwdomg  9534  xpwdomg  9535  wdomfil  10019  isfin32i  10324  hsmexlem1  10385  hsmexlem3  10387  wdomac  10486