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Mirrors > Home > ILE Home > Th. List > lpowlpo | GIF version |
Description: LPO implies WLPO. Easy corollary of the more general omniwomnimkv 7093. There is an analogue in terms of analytic omniscience principles at tridceq 13590. (Contributed by Jim Kingdon, 24-Jul-2024.) |
Ref | Expression |
---|---|
lpowlpo | ⊢ (ω ∈ Omni → ω ∈ WOmni) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omniwomnimkv 7093 | . 2 ⊢ (ω ∈ Omni ↔ (ω ∈ WOmni ∧ ω ∈ Markov)) | |
2 | 1 | simplbi 272 | 1 ⊢ (ω ∈ Omni → ω ∈ WOmni) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2128 ωcom 4547 Omnicomni 7060 Markovcmarkov 7077 WOmnicwomni 7089 |
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 4330 df-fn 5170 df-f 5171 df-1o 6357 df-omni 7061 df-markov 7078 df-womni 7090 |
This theorem is referenced by: (None) |
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