omnimkv - Intuitionistic Logic Explorer

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Theorem omnimkv 7082

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 7062	. . . 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 1859	. . 3 Omni $\/$
8	2, 7	mpd 13	. 2 Omni
9		ismkv 7079	. 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 1333

wceq 1335

wcel 2128

wral 2435

wrex 2436

c0 3394

wf 5163

cfv 5167

c1o 6350

c2o 6351 Omnicomni 7060 Markovcmarkov 7077

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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139

This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-fn 5170 df-f 5171 df-omni 7061 df-markov 7078

This theorem is referenced by: exmidmp 7083