Theorem lpowlpo 7105

Description: LPO implies WLPO. Easy corollary of the more general omniwomnimkv 7104. There is an analogue in terms of analytic omniscience principles at tridceq 13598. (Contributed by Jim Kingdon, 24-Jul-2024.)

Assertion

Ref	Expression
lpowlpo	|- ( om e. Omni -> om e. WOmni )

Proof of Theorem lpowlpo

Step	Hyp	Ref	Expression
1		omniwomnimkv 7104	. 2 |- ( om e. Omni <-> ( om e. WOmni /\ om e. Markov ) )
2	1	simplbi 272	1 |- ( om e. Omni -> om e. WOmni )

Syntax hints:   -> wi 4   e. wcel 2128   omcom 4548  Omnicomni 7071  Markovcmarkov 7088  WOmnicwomni 7100

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  ax-nul 4090

This theorem depends on definitions:  df-bi 116  df-dc 821  df-tru 1338  df-fal 1341  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ne 2328  df-ral 2440  df-rex 2441  df-v 2714  df-dif 3104  df-un 3106  df-nul 3395  df-sn 3566  df-suc 4331  df-fn 5172  df-f 5173  df-1o 6360  df-omni 7072  df-markov 7089  df-womni 7101

This theorem is referenced by: (None)