Theorem relae 32108

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.

Step	Hyp	Ref	Expression
1		df-ae 32107	. 2 ⊢ a.e. = {⟨𝑎, 𝑚⟩ ∣ (𝑚‘(∪ dom 𝑚 ∖ 𝑎)) = 0}
2	1	relopabiv 5719	1 ⊢ Rel a.e.

Syntax hints:   = wceq 1539   ∖ cdif 3880  ∪ cuni 4836  dom cdm 5580  Rel wrel 5585  ‘cfv 6418  0cc0 10802  a.e.cae 32105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-opab 5133  df-xp 5586  df-rel 5587  df-ae 32107

This theorem is referenced by: (None)