Theorem relae 32236

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 32235	. 2 ⊢ a.e. = {⟨𝑎, 𝑚⟩ ∣ (𝑚‘(∪ dom 𝑚 ∖ 𝑎)) = 0}
2	1	relopabiv 5733	1 ⊢ Rel a.e.

Syntax hints:   = wceq 1537   ∖ cdif 3886  ∪ cuni 4841  dom cdm 5591  Rel wrel 5596  ‘cfv 6447  0cc0 10899  a.e.cae 32233

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2103  ax-9 2111  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1540  df-ex 1778  df-sb 2063  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3436  df-in 3896  df-ss 3906  df-opab 5140  df-xp 5597  df-rel 5598  df-ae 32235

This theorem is referenced by: (None)