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Theorem fnerel 35218
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 35217 . 2 Fne = {⟨𝑥, 𝑦⟩ ∣ ( 𝑥 = 𝑦 ∧ ∀𝑧𝑥 𝑧 (𝑦 ∩ 𝒫 𝑧))}
21relopabiv 5820 1 Rel Fne
Colors of variables: wff setvar class
Syntax hints:  wa 396   = wceq 1541  wral 3061  cin 3947  wss 3948  𝒫 cpw 4602   cuni 4908  Rel wrel 5681  Fnecfne 35216
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-in 3955  df-ss 3965  df-opab 5211  df-xp 5682  df-rel 5683  df-fne 35217
This theorem is referenced by:  isfne  35219  isfne4  35220  fnetr  35231  fneval  35232  fneer  35233  fnessref  35237
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