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Theorem relae 31517
 Description: 'almost everywhere' is a relation. (Contributed by Thierry Arnoux, 20-Oct-2017.)
Assertion
Ref Expression
relae Rel a.e.

Proof of Theorem relae
Dummy variables 𝑚 𝑎 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ae 31516 . 2 a.e. = {⟨𝑎, 𝑚⟩ ∣ (𝑚‘( dom 𝑚𝑎)) = 0}
21relopabi 5675 1 Rel a.e.
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∖ cdif 3915  ∪ cuni 4819  dom cdm 5536  Rel wrel 5541  ‘cfv 6336  0cc0 10522  a.e.cae 31514 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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-rab 3141  df-v 3481  df-dif 3921  df-un 3923  df-in 3925  df-ss 3935  df-nul 4275  df-if 4449  df-sn 4549  df-pr 4551  df-op 4555  df-opab 5110  df-xp 5542  df-rel 5543  df-ae 31516 This theorem is referenced by: (None)
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