omnimkv - Intuitionistic Logic Explorer

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Theorem omnimkv 7217

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 7197	. . . 4 Omni Omni $\/$
2	1	ibi 176	. . 3 Omni $\/$
3		pm2.53 723	. . . . . . 7 $\/$
4	3	orcoms 731	. . . . . 6 $\/$
5	4	a1i 9	. . . . 5 Omni $\/$
6	5	imim2d 54	. . . 4 Omni $\/$
7	6	alimdv 1890	. . 3 Omni $\/$
8	2, 7	mpd 13	. 2 Omni
9		ismkv 7214	. 2 Omni Markov
10	8, 9	mpbird 167	1 Omni Markov

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 709

wal 1362

wceq 1364

wcel 2164

wral 2472

wrex 2473

c0 3447

wf 5251

cfv 5255

c1o 6464

c2o 6465 Omnicomni 7195 Markovcmarkov 7212

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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175

This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-rex 2478 df-v 2762 df-fn 5258 df-f 5259 df-omni 7196 df-markov 7213

This theorem is referenced by: exmidmp 7218