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Mirrors > Home > ILE Home > Th. List > exmid0el | Unicode version |
Description: Excluded middle is equivalent to decidability of being an element of an arbitrary set. (Contributed by Jim Kingdon, 18-Jun-2022.) |
Ref | Expression |
---|---|
exmid0el | EXMID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmidexmid 4090 | . . 3 EXMID DECID | |
2 | 1 | alrimiv 1830 | . 2 EXMID DECID |
3 | ax-1 6 | . . . 4 DECID DECID | |
4 | 3 | alimi 1416 | . . 3 DECID DECID |
5 | df-exmid 4089 | . . 3 EXMID DECID | |
6 | 4, 5 | sylibr 133 | . 2 DECID EXMID |
7 | 2, 6 | impbii 125 | 1 EXMID DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 DECID wdc 804 wal 1314 wcel 1465 wss 3041 c0 3333 csn 3497 EXMIDwem 4088 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-nul 4024 ax-pow 4068 |
This theorem depends on definitions: df-bi 116 df-dc 805 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rab 2402 df-v 2662 df-dif 3043 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-exmid 4089 |
This theorem is referenced by: exmidel 4098 |
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