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Theorem omnimkv 7201

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 7181	. . . 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 1890	. . 3 Omni $\/$
8	2, 7	mpd 13	. 2 Omni
9		ismkv 7198	. 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 2160

wral 2468

wrex 2469

c0 3442

wf 5238

cfv 5242

c1o 6449

c2o 6450 Omnicomni 7179 Markovcmarkov 7196

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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171

This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2758 df-fn 5245 df-f 5246 df-omni 7180 df-markov 7197

This theorem is referenced by: exmidmp 7202