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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 |
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nnred.1 |
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Ref | Expression |
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peano2nnd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnred.1 |
. 2
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2 | peano2nn 8933 |
. 2
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3 | 1, 2 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4123 ax-cnex 7904 ax-resscn 7905 ax-1re 7907 ax-addrcl 7910 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2741 df-un 3135 df-in 3137 df-ss 3144 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-br 4006 df-iota 5180 df-fv 5226 df-ov 5880 df-inn 8922 |
This theorem is referenced by: exp3vallem 10523 bcpasc 10748 caucvgre 10992 resqrexlemdecn 11023 cvgratnnlemmn 11535 cvgratnnlemseq 11536 cvgratnnlemabsle 11537 eftlub 11700 eirraplem 11786 infpnlem1 12359 infpnlem2 12360 1arith 12367 oddennn 12395 exmidunben 12429 nninfdclemp1 12453 nninfdclemlt 12454 lgsdilem2 14522 cvgcmp2nlemabs 14865 trilpolemeq1 14873 trilpolemlt1 14874 nconstwlpolemgt0 14897 |
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