Theorem relwdom 9578

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 9577	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5799	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 847   = wceq 1540  ∃wex 1779  ∅c0 4308  Rel wrel 5659  –onto→wfo 6528   ≼^* cwdom 9576

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-v 3461  df-ss 3943  df-opab 5182  df-xp 5660  df-rel 5661  df-wdom 9577

This theorem is referenced by:  brwdom  9579  brwdomi  9580  brwdomn0  9581  wdomtr  9587  wdompwdom  9590  canthwdom  9591  brwdom3i  9595  unwdomg  9596  xpwdomg  9597  wdomfil  10073  isfin32i  10377  hsmexlem1  10438  hsmexlem3  10440  wdomac  10539