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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 4170 | . . 3 EXMID DECID | |
2 | 1 | alrimiv 1861 | . 2 EXMID DECID |
3 | ax-1 6 | . . . 4 DECID DECID | |
4 | 3 | alimi 1442 | . . 3 DECID DECID |
5 | df-exmid 4169 | . . 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 824 wal 1340 wcel 2135 wss 3112 c0 3405 csn 3571 EXMIDwem 4168 |
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-14 2138 ax-ext 2146 ax-sep 4095 ax-nul 4103 ax-pow 4148 |
This theorem depends on definitions: df-bi 116 df-dc 825 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rab 2451 df-v 2724 df-dif 3114 df-in 3118 df-ss 3125 df-nul 3406 df-pw 3556 df-sn 3577 df-exmid 4169 |
This theorem is referenced by: exmidel 4179 |
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