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Mirrors > Home > ILE Home > Th. List > pw1dc0el | Unicode version |
Description: Another equivalent of excluded middle, which is a mere reformulation of the definition. (Contributed by BJ, 9-Aug-2024.) |
Ref | Expression |
---|---|
pw1dc0el | EXMID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df1o2 6373 | . . . . . . 7 | |
2 | 1 | eqcomi 2161 | . . . . . 6 |
3 | 2 | sseq2i 3155 | . . . . 5 |
4 | velpw 3550 | . . . . 5 | |
5 | 3, 4 | bitr4i 186 | . . . 4 |
6 | 5 | imbi1i 237 | . . 3 DECID DECID |
7 | 6 | albii 1450 | . 2 DECID DECID |
8 | df-exmid 4156 | . 2 EXMID DECID | |
9 | df-ral 2440 | . 2 DECID DECID | |
10 | 7, 8, 9 | 3bitr4i 211 | 1 EXMID DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 DECID wdc 820 wal 1333 wcel 2128 wral 2435 wss 3102 c0 3394 cpw 3543 csn 3560 EXMIDwem 4155 c1o 6353 |
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-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-exmid 4156 df-suc 4331 df-1o 6360 |
This theorem is referenced by: pw1dc1 6855 |
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