Theorem relwdom 9538

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 9537	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabiv 5795	1 ⊢ Rel ≼*

This proof depends on syntax axioms:   ∨ wo 861   = wceq 1570  ∃wex 1812  ∅c0 4279  Rel wrel 5653  –onto→wfo 6526   ≼^* cwdom 9536

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3916  df-opab 5168  df-xp 5654  df-rel 5655  df-wdom 9537

This theorem is used by:  brwdom  9539  brwdomi  9540  brwdomn0  9541  wdomtr  9547  wdompwdom  9550  canthwdom  9551  brwdom3i  9555  unwdomg  9556  xpwdomg  9557  wdomfil  10097  isfin32i  10400  hsmexlem1  10461  hsmexlem3  10463  wdomac  10563