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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 6408 | . . . . . . 7 | |
2 | 1 | eqcomi 2174 | . . . . . 6 |
3 | 2 | sseq2i 3174 | . . . . 5 |
4 | velpw 3573 | . . . . 5 | |
5 | 3, 4 | bitr4i 186 | . . . 4 |
6 | 5 | imbi1i 237 | . . 3 DECID DECID |
7 | 6 | albii 1463 | . 2 DECID DECID |
8 | df-exmid 4181 | . 2 EXMID DECID | |
9 | df-ral 2453 | . 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 829 wal 1346 wcel 2141 wral 2448 wss 3121 c0 3414 cpw 3566 csn 3583 EXMIDwem 4180 c1o 6388 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3568 df-exmid 4181 df-suc 4356 df-1o 6395 |
This theorem is referenced by: pw1dc1 6891 |
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