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Mirrors > Home > ILE Home > Th. List > omnimkv | Unicode version |
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.) |
Ref | Expression |
---|---|
omnimkv | Omni Markov |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isomni 7008 | . . . 4 Omni Omni | |
2 | 1 | ibi 175 | . . 3 Omni |
3 | pm2.53 711 | . . . . . . 7 | |
4 | 3 | orcoms 719 | . . . . . 6 |
5 | 4 | a1i 9 | . . . . 5 Omni |
6 | 5 | imim2d 54 | . . . 4 Omni |
7 | 6 | alimdv 1851 | . . 3 Omni |
8 | 2, 7 | mpd 13 | . 2 Omni |
9 | ismkv 7027 | . 2 Omni Markov | |
10 | 8, 9 | mpbird 166 | 1 Omni Markov |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 697 wal 1329 wceq 1331 wcel 1480 wral 2416 wrex 2417 c0 3363 wf 5119 cfv 5123 c1o 6306 c2o 6307 Omnicomni 7004 Markovcmarkov 7025 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-fn 5126 df-f 5127 df-omni 7006 df-markov 7026 |
This theorem is referenced by: exmidmp 7031 |
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