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Mirrors > Home > ILE Home > Th. List > 4nn | Unicode version |
Description: 4 is a positive integer. (Contributed by NM, 8-Jan-2006.) |
Ref | Expression |
---|---|
4nn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 8781 | . 2 | |
2 | 3nn 8882 | . . 3 | |
3 | peano2nn 8732 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | eqeltri 2212 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 (class class class)co 5774 c1 7621 caddc 7623 cn 8720 c3 8772 c4 8773 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-cnex 7711 ax-resscn 7712 ax-1re 7714 ax-addrcl 7717 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 df-inn 8721 df-2 8779 df-3 8780 df-4 8781 |
This theorem is referenced by: 5nn 8884 4nn0 8996 4z 9084 fldiv4p1lem1div2 10078 iexpcyc 10397 resqrexlemnmsq 10789 ef01bndlem 11463 flodddiv4 11631 flodddiv4t2lthalf 11634 6lcm4e12 11768 starvndx 12078 starvid 12079 starvslid 12080 srngstrd 12081 dveflem 12855 tan4thpi 12922 |
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