Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > exmidmp | GIF version |
Description: Excluded middle implies Markov's Principle (MP). (Contributed by Jim Kingdon, 4-Apr-2023.) |
Ref | Expression |
---|---|
exmidmp | ⊢ (EXMID → ω ∈ Markov) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmidlpo 7098 | . 2 ⊢ (EXMID → ω ∈ Omni) | |
2 | omnimkv 7111 | . 2 ⊢ (ω ∈ Omni → ω ∈ Markov) | |
3 | 1, 2 | syl 14 | 1 ⊢ (EXMID → ω ∈ Markov) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2135 EXMIDwem 4167 ωcom 4561 Omnicomni 7089 Markovcmarkov 7106 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-nul 4102 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-iinf 4559 |
This theorem depends on definitions: df-bi 116 df-dc 825 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-sbc 2947 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-nul 3405 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-br 3977 df-opab 4038 df-mpt 4039 df-exmid 4168 df-id 4265 df-suc 4343 df-iom 4562 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-iota 5147 df-fun 5184 df-fn 5185 df-f 5186 df-fv 5190 df-1o 6375 df-2o 6376 df-omni 7090 df-markov 7107 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |