Theorem relwdom 9526

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 9525	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5786	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 847   = wceq 1540  ∃wex 1779  ∅c0 4299  Rel wrel 5646  –onto→wfo 6512   ≼^* cwdom 9524

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 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-ss 3934  df-opab 5173  df-xp 5647  df-rel 5648  df-wdom 9525

This theorem is referenced by:  brwdom  9527  brwdomi  9528  brwdomn0  9529  wdomtr  9535  wdompwdom  9538  canthwdom  9539  brwdom3i  9543  unwdomg  9544  xpwdomg  9545  wdomfil  10021  isfin32i  10325  hsmexlem1  10386  hsmexlem3  10388  wdomac  10487