Theorem relwdom 9325

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 9324	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5730	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 844   = wceq 1539  ∃wex 1782  ∅c0 4256  Rel wrel 5594  –onto→wfo 6431   ≼^* cwdom 9323

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-opab 5137  df-xp 5595  df-rel 5596  df-wdom 9324

This theorem is referenced by:  brwdom  9326  brwdomi  9327  brwdomn0  9328  wdomtr  9334  wdompwdom  9337  canthwdom  9338  brwdom3i  9342  unwdomg  9343  xpwdomg  9344  wdomfil  9817  isfin32i  10121  hsmexlem1  10182  hsmexlem3  10184  wdomac  10283