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Theorem omnimkv 7082
 Description: An omniscient set is Markov. In particular, the case where is means that the Limited Principle of Omniscience (LPO) implies Markov's Principle (MP). (Contributed by Jim Kingdon, 18-Mar-2023.)
Assertion
Ref Expression
omnimkv Omni Markov

Proof of Theorem omnimkv
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 isomni 7062 . . . 4 Omni Omni
21ibi 175 . . 3 Omni
3 pm2.53 712 . . . . . . 7
43orcoms 720 . . . . . 6
54a1i 9 . . . . 5 Omni
65imim2d 54 . . . 4 Omni
76alimdv 1859 . . 3 Omni
82, 7mpd 13 . 2 Omni
9 ismkv 7079 . 2 Omni Markov
108, 9mpbird 166 1 Omni Markov
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 698  wal 1333   wceq 1335   wcel 2128  wral 2435  wrex 2436  c0 3394  wf 5163  cfv 5167  c1o 6350  c2o 6351  Omnicomni 7060  Markovcmarkov 7077 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-fn 5170  df-f 5171  df-omni 7061  df-markov 7078 This theorem is referenced by:  exmidmp  7083
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