Theorem relae 34873

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 34872	. 2 ⊢ a.e. = {⟨𝑎, 𝑚⟩ ∣ (𝑚‘(∪ dom 𝑚 ∖ 𝑎)) = 0}
2	1	relopabiv 5797	1 ⊢ Rel a.e.

This proof depends on syntax axioms:   = wceq 1569   ∖ cdif 4045  ∪ cuni 4866  dom cdm 5650  Rel wrel 5655  ‘cfv 6538  0cc0 11200  a.e.cae 34870

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-opab 5167  df-xp 5656  df-rel 5657  df-ae 34872

This theorem is used by: (None)