Theorem relwdom 9423

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 9422	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5762	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 844   = wceq 1540  ∃wex 1780  ∅c0 4269  Rel wrel 5625  –onto→wfo 6477   ≼^* cwdom 9421

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 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443  df-in 3905  df-ss 3915  df-opab 5155  df-xp 5626  df-rel 5627  df-wdom 9422

This theorem is referenced by:  brwdom  9424  brwdomi  9425  brwdomn0  9426  wdomtr  9432  wdompwdom  9435  canthwdom  9436  brwdom3i  9440  unwdomg  9441  xpwdomg  9442  wdomfil  9918  isfin32i  10222  hsmexlem1  10283  hsmexlem3  10285  wdomac  10384