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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 9009 |
. 2
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2 | 3nn 9110 |
. . 3
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3 | peano2nn 8960 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | 1, 4 | eqeltri 2262 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4136 ax-cnex 7931 ax-resscn 7932 ax-1re 7934 ax-addrcl 7937 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5898 df-inn 8949 df-2 9007 df-3 9008 df-4 9009 |
This theorem is referenced by: 5nn 9112 4nn0 9224 4z 9312 fldiv4p1lem1div2 10335 iexpcyc 10655 resqrexlemnmsq 11057 ef01bndlem 11795 flodddiv4 11970 flodddiv4t2lthalf 11973 6lcm4e12 12118 starvndx 12647 starvid 12648 starvslid 12649 srngstrd 12654 homid 12737 homslid 12738 dveflem 14639 tan4thpi 14714 m1lgs 14905 |
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