Theorem relwdom 9495

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 9494	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5774	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 847   = wceq 1540  ∃wex 1779  ∅c0 4292  Rel wrel 5636  –onto→wfo 6497   ≼^* cwdom 9493

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 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3446  df-ss 3928  df-opab 5165  df-xp 5637  df-rel 5638  df-wdom 9494

This theorem is referenced by:  brwdom  9496  brwdomi  9497  brwdomn0  9498  wdomtr  9504  wdompwdom  9507  canthwdom  9508  brwdom3i  9512  unwdomg  9513  xpwdomg  9514  wdomfil  9990  isfin32i  10294  hsmexlem1  10355  hsmexlem3  10357  wdomac  10456