Theorem relwdom 8762

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 8755	. 2 ⊢ ≼* = {⟨𝑥, 𝑦⟩ ∣ (𝑥 = ∅ ∨ ∃𝑧 𝑧:𝑦–onto→𝑥)}
2	1	relopabi 5493	1 ⊢ Rel ≼*

Syntax hints:   ∨ wo 836   = wceq 1601  ∃wex 1823  ∅c0 4141  Rel wrel 5362  –onto→wfo 6135   ≼^* cwdom 8753

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-13 2334  ax-ext 2754

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-rab 3099  df-v 3400  df-dif 3795  df-un 3797  df-in 3799  df-ss 3806  df-nul 4142  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-opab 4951  df-xp 5363  df-rel 5364  df-wdom 8755

This theorem is referenced by:  brwdom  8763  brwdomi  8764  brwdomn0  8765  wdomtr  8771  wdompwdom  8774  canthwdom  8775  brwdom3i  8779  unwdomg  8780  xpwdomg  8781  wdomfil  9219  isfin32i  9524  hsmexlem1  9585  hsmexlem3  9587  wdomac  9686