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Mirrors > Home > ILE Home > Th. List > peano2nnd | Unicode version |
Description: Peano postulate: a successor of a positive integer is a positive integer. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
nnred.1 |
Ref | Expression |
---|---|
peano2nnd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnred.1 | . 2 | |
2 | peano2nn 8860 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 (class class class)co 5836 c1 7745 caddc 7747 cn 8848 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-sep 4094 ax-cnex 7835 ax-resscn 7836 ax-1re 7838 ax-addrcl 7841 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-br 3977 df-iota 5147 df-fv 5190 df-ov 5839 df-inn 8849 |
This theorem is referenced by: exp3vallem 10446 bcpasc 10668 caucvgre 10909 resqrexlemdecn 10940 cvgratnnlemmn 11452 cvgratnnlemseq 11453 cvgratnnlemabsle 11454 eftlub 11617 eirraplem 11703 oddennn 12268 exmidunben 12302 nninfdclemp1 12328 nninfdclemlt 12329 cvgcmp2nlemabs 13752 trilpolemeq1 13760 trilpolemlt1 13761 nconstwlpolemgt0 13783 |
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