Theorem lpowlpo 7502

Description: LPO implies WLPO. Easy corollary of the more general omniwomnimkv 7501. There is an analogue in terms of analytic omniscience principles at tridceq 17080. (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 7501	. 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 2209   omcom 4735  Omnicomni 7468  Markovcmarkov 7485  WOmnicwomni 7497

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 623  ax-in2 624  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220  ax-nul 4257

This theorem depends on definitions:  df-bi 117  df-dc 847  df-tru 1405  df-fal 1408  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-ne 2421  df-ral 2533  df-rex 2534  df-v 2823  df-dif 3222  df-un 3224  df-nul 3521  df-sn 3714  df-suc 4514  df-fn 5378  df-f 5379  df-1o 6681  df-omni 7469  df-markov 7486  df-womni 7498

This theorem is referenced by:  nnnninfen  17038