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Mirrors > Home > ILE Home > Th. List > 0nnn | Unicode version |
Description: Zero is not a positive integer. (Contributed by NM, 25-Aug-1999.) |
Ref | Expression |
---|---|
0nnn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0lt1 8078 |
. 2
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2 | nnnlt1 8939 |
. 2
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3 | 1, 2 | mt2 640 |
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-in1 614 ax-in2 615 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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4119 ax-pow 4172 ax-pr 4207 ax-un 4431 ax-setind 4534 ax-cnex 7897 ax-resscn 7898 ax-1re 7900 ax-addrcl 7903 ax-0lt1 7912 ax-0id 7914 ax-rnegex 7915 ax-pre-ltirr 7918 ax-pre-lttrn 7920 ax-pre-ltadd 7922 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3809 df-int 3844 df-br 4002 df-opab 4063 df-xp 4630 df-cnv 4632 df-iota 5175 df-fv 5221 df-ov 5873 df-pnf 7988 df-mnf 7989 df-xr 7990 df-ltxr 7991 df-le 7992 df-inn 8914 |
This theorem is referenced by: nnne0 8941 dfn2 9183 nn0enne 11897 exprmfct 12128 coprm 12134 |
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