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Theorem relae 34219
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 34218 . 2 a.e. = {⟨𝑎, 𝑚⟩ ∣ (𝑚‘( dom 𝑚𝑎)) = 0}
21relopabiv 5828 1 Rel a.e.
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cdif 3947   cuni 4905  dom cdm 5683  Rel wrel 5688  cfv 6559  0cc0 11151  a.e.cae 34216
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-ss 3967  df-opab 5204  df-xp 5689  df-rel 5690  df-ae 34218
This theorem is referenced by: (None)
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