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Theorem relae 32903
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 32902 . 2 a.e. = {⟨𝑎, 𝑚⟩ ∣ (𝑚‘( dom 𝑚𝑎)) = 0}
21relopabiv 5780 1 Rel a.e.
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cdif 3911   cuni 4869  dom cdm 5637  Rel wrel 5642  cfv 6500  0cc0 11059  a.e.cae 32900
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 3449  df-in 3921  df-ss 3931  df-opab 5172  df-xp 5643  df-rel 5644  df-ae 32902
This theorem is referenced by: (None)
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