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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 8899 | . 2 | |
2 | 2nn 9000 | . . 3 | |
3 | peano2nn 8851 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | eqeltri 2230 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2128 (class class class)co 5827 c1 7736 caddc 7738 cn 8839 c2 8890 c3 8891 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-sep 4085 ax-cnex 7826 ax-resscn 7827 ax-1re 7829 ax-addrcl 7832 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-int 3810 df-br 3968 df-iota 5138 df-fv 5181 df-ov 5830 df-inn 8840 df-2 8898 df-3 8899 |
This theorem is referenced by: 4nn 9002 3nn0 9114 3z 9202 ige3m2fz 9958 sin01bnd 11666 3lcm2e6woprm 11979 3lcm2e6 12051 mulrndx 12396 mulrid 12397 mulrslid 12398 rngstrg 12401 tangtx 13255 |
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