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Theorem fnerel 36321
Description: Fineness is a relation. (Contributed by Jeff Hankins, 28-Sep-2009.)
Assertion
Ref Expression
fnerel Rel Fne

Proof of Theorem fnerel
Dummy variables 𝑥 𝑦 𝑧 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-fne 36320 . 2 Fne = {⟨𝑥, 𝑦⟩ ∣ ( 𝑥 = 𝑦 ∧ ∀𝑧𝑥 𝑧 (𝑦 ∩ 𝒫 𝑧))}
21relopabiv 5833 1 Rel Fne
Colors of variables: wff setvar class
Syntax hints:  wa 395   = wceq 1537  wral 3059  cin 3962  wss 3963  𝒫 cpw 4605   cuni 4912  Rel wrel 5694  Fnecfne 36319
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-opab 5211  df-xp 5695  df-rel 5696  df-fne 36320
This theorem is referenced by:  isfne  36322  isfne4  36323  fnetr  36334  fneval  36335  fneer  36336  fnessref  36340
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