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Theorem elprob 28545
 Description: The property of being a probability measure (Contributed by Thierry Arnoux, 8-Dec-2016.)
Assertion
Ref Expression
elprob Prob measures

Proof of Theorem elprob
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 id 22 . . . 4
2 dmeq 5213 . . . . 5
32unieqd 4261 . . . 4
41, 3fveq12d 5878 . . 3
54eqeq1d 2459 . 2
6 df-prob 28544 . 2 Prob measures
75, 6elrab2 3259 1 Prob measures
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1395   wcel 1819  cuni 4251   cdm 5008   crn 5009  cfv 5594  c1 9510  measurescmeas 28339  Probcprb 28543 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-dm 5018  df-iota 5557  df-fv 5602  df-prob 28544 This theorem is referenced by:  domprobmeas  28546  probtot  28548  probfinmeasbOLD  28564  probfinmeasb  28565  probmeasb  28566  dstrvprob  28607
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