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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 8700 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 (class class class)co 5742 c1 7589 caddc 7591 cn 8688 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-cnex 7679 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-int 3742 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-inn 8689 |
This theorem is referenced by: exp3vallem 10262 bcpasc 10480 caucvgre 10721 resqrexlemdecn 10752 cvgratnnlemmn 11262 cvgratnnlemseq 11263 cvgratnnlemabsle 11264 eftlub 11323 eirraplem 11410 oddennn 11832 exmidunben 11866 cvgcmp2nlemabs 13154 trilpolemeq1 13160 trilpolemlt1 13161 |
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