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Theorem brae 29016
 Description: 'almost everywhere' relation for a measure and a measurable set . (Contributed by Thierry Arnoux, 20-Oct-2017.)
Assertion
Ref Expression
brae measures a.e.

Proof of Theorem brae
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 simpr 462 . . . . 5
21dmeqd 4999 . . . . . . 7
32unieqd 4172 . . . . . 6
4 simpl 458 . . . . . 6
53, 4difeq12d 3527 . . . . 5
61, 5fveq12d 5831 . . . 4
76eqeq1d 2430 . . 3
8 df-ae 29014 . . 3 a.e.
97, 8brabga 4677 . 2 measures a.e.
109ancoms 454 1 measures a.e.
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437   wcel 1872   cdif 3376  cuni 4162   class class class wbr 4366   cdm 4796   crn 4797  cfv 5544  cc0 9490  measurescmeas 28969  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-eu 2280  df-mo 2281  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-uni 4163  df-br 4367  df-opab 4426  df-dm 4806  df-iota 5508  df-fv 5552  df-ae 29014 This theorem is referenced by: (None)
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