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Theorem omnimkv 7258

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 7238	. . . 4 Omni Omni $\/$
2	1	ibi 176	. . 3 Omni $\/$
3		pm2.53 724	. . . . . . 7 $\/$
4	3	orcoms 732	. . . . . 6 $\/$
5	4	a1i 9	. . . . 5 Omni $\/$
6	5	imim2d 54	. . . 4 Omni $\/$
7	6	alimdv 1902	. . 3 Omni $\/$
8	2, 7	mpd 13	. 2 Omni
9		ismkv 7255	. 2 Omni Markov
10	8, 9	mpbird 167	1 Omni Markov

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 710

wal 1371

wceq 1373

wcel 2176

wral 2484

wrex 2485

c0 3460

wf 5267

cfv 5271

c1o 6495

c2o 6496 Omnicomni 7236 Markovcmarkov 7253

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 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-ext 2187

This theorem depends on definitions: df-bi 117 df-tru 1376 df-nf 1484 df-sb 1786 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ral 2489 df-rex 2490 df-v 2774 df-fn 5274 df-f 5275 df-omni 7237 df-markov 7254

This theorem is referenced by: exmidmp 7259