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Mirrors > Home > ILE Home > Th. List > exmidontri | Unicode version |
Description: Ordinal trichotomy is equivalent to excluded middle. (Contributed by Jim Kingdon, 26-Aug-2024.) |
Ref | Expression |
---|---|
exmidontri | EXMID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmidontriim 7161 | . 2 EXMID | |
2 | ontriexmidim 4482 | . . . 4 DECID | |
3 | 2 | adantr 274 | . . 3 DECID |
4 | 3 | exmid1dc 4162 | . 2 EXMID |
5 | 1, 4 | impbii 125 | 1 EXMID |
Colors of variables: wff set class |
Syntax hints: wb 104 DECID wdc 820 w3o 962 wceq 1335 wral 2435 wss 3102 c0 3394 csn 3560 EXMIDwem 4156 con0 4324 |
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-14 2131 ax-ext 2139 ax-sep 4083 ax-nul 4091 ax-pow 4136 ax-setind 4497 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-3or 964 df-3an 965 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-rab 2444 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-uni 3774 df-tr 4064 df-exmid 4157 df-iord 4327 df-on 4329 df-suc 4332 |
This theorem is referenced by: (None) |
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