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Mirrors > Home > ILE Home > Th. List > nsuceq0g | Unicode version |
Description: No successor is empty. (Contributed by Jim Kingdon, 14-Oct-2018.) |
Ref | Expression |
---|---|
nsuceq0g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3418 | . . 3 | |
2 | sucidg 4401 | . . . 4 | |
3 | eleq2 2234 | . . . 4 | |
4 | 2, 3 | syl5ibcom 154 | . . 3 |
5 | 1, 4 | mtoi 659 | . 2 |
6 | 5 | neneqad 2419 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 wne 2340 c0 3414 csuc 4350 |
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-ne 2341 df-v 2732 df-dif 3123 df-un 3125 df-nul 3415 df-sn 3589 df-suc 4356 |
This theorem is referenced by: onsucelsucexmid 4514 peano3 4580 frec0g 6376 2on0 6405 zfz1iso 10776 |
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