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Mirrors > Home > ILE Home > Th. List > 10nn | Unicode version |
Description: 10 is a positive integer. (Contributed by NM, 8-Nov-2012.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
10nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9p1e10 9381 |
. 2
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2 | 9nn 9082 |
. . 3
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3 | peano2nn 8926 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | 1, 4 | eqeltrri 2251 |
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 4120 ax-cnex 7898 ax-resscn 7899 ax-1cn 7900 ax-1re 7901 ax-icn 7902 ax-addcl 7903 ax-addrcl 7904 ax-mulcl 7905 ax-mulcom 7908 ax-addass 7909 ax-mulass 7910 ax-distr 7911 ax-1rid 7914 ax-0id 7915 ax-cnre 7918 |
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-rab 2464 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4003 df-iota 5176 df-fv 5222 df-ov 5874 df-inn 8915 df-2 8973 df-3 8974 df-4 8975 df-5 8976 df-6 8977 df-7 8978 df-8 8979 df-9 8980 df-dec 9380 |
This theorem is referenced by: 10pos 9395 10re 9397 decnncl2 9402 declt 9406 decltc 9407 declti 9416 dec10p 9421 plendx 12646 pleid 12647 pleslid 12648 plendxnn 12649 |
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