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.

Step	Hyp	Ref	Expression
1		df-ae 34218	. 2 ⊢ a.e. = {⟨𝑎, 𝑚⟩ ∣ (𝑚‘(∪ dom 𝑚 ∖ 𝑎)) = 0}
2	1	relopabiv 5828	1 ⊢ Rel a.e.

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)