Theorem relwdom 9032

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 9025	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabi 5696	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 843   = wceq 1537  ∃wex 1780  ∅c0 4293  Rel wrel 5562  –onto→wfo 6355   ≼^* cwdom 9023

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2795

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2802  df-cleq 2816  df-clel 2895  df-nfc 2965  df-rab 3149  df-v 3498  df-dif 3941  df-un 3943  df-in 3945  df-ss 3954  df-nul 4294  df-if 4470  df-sn 4570  df-pr 4572  df-op 4576  df-opab 5131  df-xp 5563  df-rel 5564  df-wdom 9025

This theorem is referenced by:  brwdom  9033  brwdomi  9034  brwdomn0  9035  wdomtr  9041  wdompwdom  9044  canthwdom  9045  brwdom3i  9049  unwdomg  9050  xpwdomg  9051  wdomfil  9489  isfin32i  9789  hsmexlem1  9850  hsmexlem3  9852  wdomac  9951