Users' Mathboxes Mathbox for Thierry Arnoux < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  relae Structured version   Unicode version

Theorem relae 29015
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.
StepHypRef Expression
1 df-ae 29014 . 2  |- a.e.  =  { <. a ,  m >.  |  ( m `  ( U. dom  m  \  a
) )  =  0 }
21relopabi 4921 1  |-  Rel a.e.
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437    \ cdif 3376   U.cuni 4162   dom cdm 4796   Rel wrel 4801   ` cfv 5544   0cc0 9490  a.e.cae 29012
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408  ax-sep 4489  ax-nul 4498  ax-pr 4603
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ne 2601  df-ral 2719  df-rex 2720  df-rab 2723  df-v 3024  df-dif 3382  df-un 3384  df-in 3386  df-ss 3393  df-nul 3705  df-if 3855  df-sn 3942  df-pr 3944  df-op 3948  df-opab 4426  df-xp 4802  df-rel 4803  df-ae 29014
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator