Theorem relwdom 9560

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 9559	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5797	1 ⊢ Rel ≼*

This proof depends on syntax axioms:   ∨ wo 861   = wceq 1569  ∃wex 1811  ∅c0 4278  Rel wrel 5655  –onto→wfo 6536   ≼^* cwdom 9558

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-opab 5167  df-xp 5656  df-rel 5657  df-wdom 9559

This theorem is used by:  brwdom  9561  brwdomi  9562  brwdomn0  9563  wdomtr  9569  wdompwdom  9572  canthwdom  9573  brwdom3i  9577  unwdomg  9578  xpwdomg  9579  wdomfil  10140  isfin32i  10443  hsmexlem1  10504  hsmexlem3  10506  wdomac  10606