Theorem lpowlpo 7270

Description: LPO implies WLPO. Easy corollary of the more general omniwomnimkv 7269. There is an analogue in terms of analytic omniscience principles at tridceq 15999. (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 7269	. 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 2176   omcom 4638  Omnicomni 7236  Markovcmarkov 7253  WOmnicwomni 7265

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  ax-nul 4170

This theorem depends on definitions:  df-bi 117  df-dc 837  df-tru 1376  df-fal 1379  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-ne 2377  df-ral 2489  df-rex 2490  df-v 2774  df-dif 3168  df-un 3170  df-nul 3461  df-sn 3639  df-suc 4418  df-fn 5274  df-f 5275  df-1o 6502  df-omni 7237  df-markov 7254  df-womni 7266

This theorem is referenced by:  nnnninfen  15962