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Mirrors > Home > ILE Home > Th. List > 3nn | Unicode version |
Description: 3 is a positive integer. (Contributed by NM, 8-Jan-2006.) |
Ref | Expression |
---|---|
3nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 8977 |
. 2
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2 | 2nn 9078 |
. . 3
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3 | peano2nn 8929 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | 1, 4 | eqeltri 2250 |
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 4121 ax-cnex 7901 ax-resscn 7902 ax-1re 7904 ax-addrcl 7907 |
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 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 4004 df-iota 5178 df-fv 5224 df-ov 5877 df-inn 8918 df-2 8976 df-3 8977 |
This theorem is referenced by: 4nn 9080 3nn0 9192 3z 9280 ige3m2fz 10046 sin01bnd 11760 3lcm2e6woprm 12080 3lcm2e6 12154 mulrndx 12582 mulridx 12583 mulrslid 12584 rngstrg 12587 unifndx 12671 unifid 12672 unifndxnn 12673 slotsdifunifndx 12677 cnfldstr 13348 tangtx 14152 lgsdir2lem1 14322 lgsdir2lem5 14326 |
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