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Mirrors > Home > ILE Home > Th. List > lpowlpo | GIF version |
Description: LPO implies WLPO. Easy corollary of the more general omniwomnimkv 7143. There is an analogue in terms of analytic omniscience principles at tridceq 14088. (Contributed by Jim Kingdon, 24-Jul-2024.) |
Ref | Expression |
---|---|
lpowlpo | ⊢ (ω ∈ Omni → ω ∈ WOmni) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omniwomnimkv 7143 | . 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 2141 ωcom 4574 Omnicomni 7110 Markovcmarkov 7127 WOmnicwomni 7139 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-nul 4115 |
This theorem depends on definitions: df-bi 116 df-dc 830 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-nul 3415 df-sn 3589 df-suc 4356 df-fn 5201 df-f 5202 df-1o 6395 df-omni 7111 df-markov 7128 df-womni 7140 |
This theorem is referenced by: (None) |
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