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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 3398 | . . 3 | |
2 | sucidg 4376 | . . . 4 | |
3 | eleq2 2221 | . . . 4 | |
4 | 2, 3 | syl5ibcom 154 | . . 3 |
5 | 1, 4 | mtoi 654 | . 2 |
6 | 5 | neneqad 2406 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wcel 2128 wne 2327 c0 3394 csuc 4325 |
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-ne 2328 df-v 2714 df-dif 3104 df-un 3106 df-nul 3395 df-sn 3566 df-suc 4331 |
This theorem is referenced by: onsucelsucexmid 4489 peano3 4555 frec0g 6344 2on0 6373 zfz1iso 10712 |
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