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Theorem omnimkv 7023

Description: An omniscient set is Markov. In particular, the case where

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.

Step	Hyp	Ref	Expression
1		isomni 7001	. . . 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 7020	. 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 2414

wrex 2415

c0 3358

wf 5114

cfv 5118

c1o 6299

c2o 6300 Omnicomni 6997 Markovcmarkov 7018

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 2119

This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-fn 5121 df-f 5122 df-omni 6999 df-markov 7019

This theorem is referenced by: exmidmp 7024