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Mirrors > Home > ILE Home > Th. List > nnsuc | Unicode version |
Description: A nonzero natural number is a successor. (Contributed by NM, 18-Feb-2004.) |
Ref | Expression |
---|---|
nnsuc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2309 | . 2 | |
2 | nn0suc 4518 | . . . 4 | |
3 | 2 | ord 713 | . . 3 |
4 | 3 | imp 123 | . 2 |
5 | 1, 4 | sylan2b 285 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1331 wcel 1480 wne 2308 wrex 2417 c0 3363 csuc 4287 com 4504 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-nul 4054 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-iinf 4502 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-uni 3737 df-int 3772 df-suc 4293 df-iom 4505 |
This theorem is referenced by: nnsucpred 4530 |
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