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Theorem omnimkv 7222

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 7202	. . . 4 Omni Omni $\/$
2	1	ibi 176	. . 3 Omni $\/$
3		pm2.53 723	. . . . . . 7 $\/$
4	3	orcoms 731	. . . . . 6 $\/$
5	4	a1i 9	. . . . 5 Omni $\/$
6	5	imim2d 54	. . . 4 Omni $\/$
7	6	alimdv 1893	. . 3 Omni $\/$
8	2, 7	mpd 13	. 2 Omni
9		ismkv 7219	. 2 Omni Markov
10	8, 9	mpbird 167	1 Omni Markov

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 709

wal 1362

wceq 1364

wcel 2167

wral 2475

wrex 2476

c0 3450

wf 5254

cfv 5258

c1o 6467

c2o 6468 Omnicomni 7200 Markovcmarkov 7217

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1461 ax-7 1462 ax-gen 1463 ax-ie1 1507 ax-ie2 1508 ax-8 1518 ax-10 1519 ax-11 1520 ax-i12 1521 ax-bndl 1523 ax-4 1524 ax-17 1540 ax-i9 1544 ax-ial 1548 ax-i5r 1549 ax-ext 2178

This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1475 df-sb 1777 df-clab 2183 df-cleq 2189 df-clel 2192 df-nfc 2328 df-ral 2480 df-rex 2481 df-v 2765 df-fn 5261 df-f 5262 df-omni 7201 df-markov 7218

This theorem is referenced by: exmidmp 7223