Theorem relwdom 9452

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 9451	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5759	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 847   = wceq 1541  ∃wex 1780  ∅c0 4280  Rel wrel 5619  –onto→wfo 6479   ≼^* cwdom 9450

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 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-ss 3914  df-opab 5152  df-xp 5620  df-rel 5621  df-wdom 9451

This theorem is referenced by:  brwdom  9453  brwdomi  9454  brwdomn0  9455  wdomtr  9461  wdompwdom  9464  canthwdom  9465  brwdom3i  9469  unwdomg  9470  xpwdomg  9471  wdomfil  9952  isfin32i  10256  hsmexlem1  10317  hsmexlem3  10319  wdomac  10418