Theorem relwdom 9526

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 9525	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5806	1 ⊢ Rel ≼*

This proof depends on syntax axioms:   ∨ wo 860   = wceq 1569  ∃wex 1808  ∅c0 4285  Rel wrel 5665  –onto→wfo 6534   ≼^* cwdom 9524

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-ss 3921  df-opab 5173  df-xp 5666  df-rel 5667  df-wdom 9525

This theorem is used by:  brwdom  9527  brwdomi  9528  brwdomn0  9529  wdomtr  9535  wdompwdom  9538  canthwdom  9539  brwdom3i  9543  unwdomg  9544  xpwdomg  9545  wdomfil  10052  isfin32i  10355  hsmexlem1  10416  hsmexlem3  10418  wdomac  10517