Theorem relwdom 9584

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 9583	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦⟶onto𝑥)}
2	1	relopabiv 5803	1 ⊢ Rel ≼*

This proof depends on syntax axioms:   ∨ wo 861   = wceq 1570  ∃wex 1812  ∅c0 4281  Rel wrel 5660  ⟶ontowfo 6553   ≼^* cwdom 9582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-opab 5171  df-xp 5661  df-rel 5662  df-wdom 9583

This theorem is used by:  brwdom  9585  brwdomi  9586  brwdomn0  9587  wdomtr  9593  wdompwdom  9596  canthwdom  9597  brwdom3i  9601  unwdomg  9602  xpwdomg  9603  wdomfil  10164  isfin32i  10467  hsmexlem1  10528  hsmexlem3  10530  wdomac  10630