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Theorem measfrge0 28040
 Description: A measure is a function over its base to the positive extended reals. (Contributed by Thierry Arnoux, 26-Dec-2016.)
Assertion
Ref Expression
measfrge0 measures

Proof of Theorem measfrge0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 measbase 28034 . . . 4 measures sigAlgebra
2 ismeas 28036 . . . 4 sigAlgebra measures Disj Σ*
31, 2syl 16 . . 3 measures measures Disj Σ*
43ibi 241 . 2 measures Disj Σ*
54simp1d 1007 1 measures
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 972   wceq 1381   wcel 1802  wral 2791  c0 3767  cpw 3993  cuni 4230  Disj wdisj 4403   class class class wbr 4433   crn 4986  wf 5570  cfv 5574  (class class class)co 6277  com 6681   cdom 7512  cc0 9490   cpnf 9623  cicc 11536  Σ*cesum 27906  sigAlgebracsiga 27973  measurescmeas 28032 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-8 1804  ax-9 1806  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419  ax-sep 4554  ax-nul 4562  ax-pow 4611  ax-pr 4672  ax-un 6573 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 974  df-tru 1384  df-fal 1387  df-ex 1598  df-nf 1602  df-sb 1725  df-eu 2270  df-mo 2271  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ne 2638  df-ral 2796  df-rex 2797  df-rab 2800  df-v 3095  df-sbc 3312  df-csb 3418  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-if 3923  df-pw 3995  df-sn 4011  df-pr 4013  df-op 4017  df-uni 4231  df-br 4434  df-opab 4492  df-mpt 4493  df-id 4781  df-xp 4991  df-rel 4992  df-cnv 4993  df-co 4994  df-dm 4995  df-rn 4996  df-iota 5537  df-fun 5576  df-fn 5577  df-f 5578  df-fv 5582  df-ov 6280  df-esum 27907  df-meas 28033 This theorem is referenced by:  measfn  28041  measvxrge0  28042  meascnbl  28056  measres  28059  measdivcstOLD  28061  measdivcst  28062
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