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Theorem fnerel 35161
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 35160 . 2 Fne = {⟨𝑥, 𝑦⟩ ∣ ( 𝑥 = 𝑦 ∧ ∀𝑧𝑥 𝑧 (𝑦 ∩ 𝒫 𝑧))}
21relopabiv 5818 1 Rel Fne
Colors of variables: wff setvar class
Syntax hints:  wa 397   = wceq 1542  wral 3062  cin 3946  wss 3947  𝒫 cpw 4601   cuni 4907  Rel wrel 5680  Fnecfne 35159
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3954  df-ss 3964  df-opab 5210  df-xp 5681  df-rel 5682  df-fne 35160
This theorem is referenced by:  isfne  35162  isfne4  35163  fnetr  35174  fneval  35175  fneer  35176  fnessref  35180
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