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Theorem omnimkv 7120

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 7100	. . . 4 Omni Omni $\/$
2	1	ibi 175	. . 3 Omni $\/$
3		pm2.53 712	. . . . . . 7 $\/$
4	3	orcoms 720	. . . . . 6 $\/$
5	4	a1i 9	. . . . 5 Omni $\/$
6	5	imim2d 54	. . . 4 Omni $\/$
7	6	alimdv 1867	. . 3 Omni $\/$
8	2, 7	mpd 13	. 2 Omni
9		ismkv 7117	. 2 Omni Markov
10	8, 9	mpbird 166	1 Omni Markov

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 698

wal 1341

wceq 1343

wcel 2136

wral 2444

wrex 2445

c0 3409

wf 5184

cfv 5188

c1o 6377

c2o 6378 Omnicomni 7098 Markovcmarkov 7115

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 604 ax-in2 605 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147

This theorem depends on definitions: df-bi 116 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ral 2449 df-rex 2450 df-v 2728 df-fn 5191 df-f 5192 df-omni 7099 df-markov 7116

This theorem is referenced by: exmidmp 7121