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Theorem omnimkv 7354

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 7334	. . . 4 Omni Omni $\/$
2	1	ibi 176	. . 3 Omni $\/$
3		pm2.53 729	. . . . . . 7 $\/$
4	3	orcoms 737	. . . . . 6 $\/$
5	4	a1i 9	. . . . 5 Omni $\/$
6	5	imim2d 54	. . . 4 Omni $\/$
7	6	alimdv 1927	. . 3 Omni $\/$
8	2, 7	mpd 13	. 2 Omni
9		ismkv 7351	. 2 Omni Markov
10	8, 9	mpbird 167	1 Omni Markov

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 715

wal 1395

wceq 1397

wcel 2202

wral 2510

wrex 2511

c0 3494

wf 5322

cfv 5326

c1o 6574

c2o 6575 Omnicomni 7332 Markovcmarkov 7349

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 619 ax-in2 620 ax-io 716 ax-5 1495 ax-7 1496 ax-gen 1497 ax-ie1 1541 ax-ie2 1542 ax-8 1552 ax-10 1553 ax-11 1554 ax-i12 1555 ax-bndl 1557 ax-4 1558 ax-17 1574 ax-i9 1578 ax-ial 1582 ax-i5r 1583 ax-ext 2213

This theorem depends on definitions: df-bi 117 df-tru 1400 df-nf 1509 df-sb 1811 df-clab 2218 df-cleq 2224 df-clel 2227 df-nfc 2363 df-ral 2515 df-rex 2516 df-v 2804 df-fn 5329 df-f 5330 df-omni 7333 df-markov 7350

This theorem is referenced by: exmidmp 7355