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Theorem omnimkv 7132

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 7112	. . . 4 Omni Omni $\/$
2	1	ibi 175	. . 3 Omni $\/$
3		pm2.53 717	. . . . . . 7 $\/$
4	3	orcoms 725	. . . . . 6 $\/$
5	4	a1i 9	. . . . 5 Omni $\/$
6	5	imim2d 54	. . . 4 Omni $\/$
7	6	alimdv 1872	. . 3 Omni $\/$
8	2, 7	mpd 13	. 2 Omni
9		ismkv 7129	. 2 Omni Markov
10	8, 9	mpbird 166	1 Omni Markov

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 703

wal 1346

wceq 1348

wcel 2141

wral 2448

wrex 2449

c0 3414

wf 5194

cfv 5198

c1o 6388

c2o 6389 Omnicomni 7110 Markovcmarkov 7127

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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152

This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-fn 5201 df-f 5202 df-omni 7111 df-markov 7128

This theorem is referenced by: exmidmp 7133