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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 |
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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 8590 |
. 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-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-cnex 7586 ax-resscn 7587 ax-1re 7589 ax-addrcl 7592 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-un 3025 df-in 3027 df-ss 3034 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-int 3719 df-br 3876 df-iota 5024 df-fv 5067 df-ov 5709 df-inn 8579 |
This theorem is referenced by: exp3vallem 10135 bcpasc 10353 caucvgre 10593 resqrexlemdecn 10624 cvgratnnlemmn 11133 cvgratnnlemseq 11134 cvgratnnlemabsle 11135 eftlub 11194 eirraplem 11278 oddennn 11697 exmidunben 11731 cvgcmp2nlemabs 12811 trilpolemeq1 12817 trilpolemlt1 12818 |
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