Theorem relwdom 9528

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 9527	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5808	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 860   = wceq 1567  ∃wex 1806  ∅c0 4292  Rel wrel 5667  –onto→wfo 6535   ≼^* cwdom 9526

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3463  df-ss 3928  df-opab 5176  df-xp 5668  df-rel 5669  df-wdom 9527

This theorem is referenced by:  brwdom  9529  brwdomi  9530  brwdomn0  9531  wdomtr  9537  wdompwdom  9540  canthwdom  9541  brwdom3i  9545  unwdomg  9546  xpwdomg  9547  wdomfil  10045  isfin32i  10349  hsmexlem1  10410  hsmexlem3  10412  wdomac  10511