Theorem relae 34940

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 34939	. 2 ⊢ a.e. = {⟨𝑎, 𝑚⟩ ∣ (𝑚‘(∪ dom 𝑚 ∖ 𝑎)) = 0}
2	1	relopabiv 5803	1 ⊢ Rel a.e.

This proof depends on syntax axioms:   = wceq 1570   ∖ cdif 4048  ∪ cuni 4870  dom cdm 5655  Rel wrel 5660  ‘cfv 6555  0cc0 11224  a.e.cae 34937

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-opab 5171  df-xp 5661  df-rel 5662  df-ae 34939

This theorem is used by: (None)