Theorem lpowlpo 7243

Description: LPO implies WLPO. Easy corollary of the more general omniwomnimkv 7242. There is an analogue in terms of analytic omniscience principles at tridceq 15787. (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 7242	. 2 |- ( om e. Omni <-> ( om e. WOmni /\ om e. Markov ) )
2	1	simplbi 274	1 |- ( om e. Omni -> om e. WOmni )

Syntax hints:   -> wi 4   e. wcel 2167   omcom 4627  Omnicomni 7209  Markovcmarkov 7226  WOmnicwomni 7238

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178  ax-nul 4160

This theorem depends on definitions:  df-bi 117  df-dc 836  df-tru 1367  df-fal 1370  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-ne 2368  df-ral 2480  df-rex 2481  df-v 2765  df-dif 3159  df-un 3161  df-nul 3452  df-sn 3629  df-suc 4407  df-fn 5262  df-f 5263  df-1o 6483  df-omni 7210  df-markov 7227  df-womni 7239

This theorem is referenced by:  nnnninfen  15752