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Theorem relae 27868
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 27867 . 2  |- a.e.  =  { <. a ,  m >.  |  ( m `  ( U. dom  m  \  a
) )  =  0 }
21relopabi 5127 1  |-  Rel a.e.
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379    \ cdif 3473   U.cuni 4245   dom cdm 4999   Rel wrel 5004   ` cfv 5587   0cc0 9491  a.e.cae 27865
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-opab 4506  df-xp 5005  df-rel 5006  df-ae 27867
This theorem is referenced by: (None)
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