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Mirrors > Home > ILE Home > Th. List > 2nn | Unicode version |
Description: 2 is a positive integer. (Contributed by NM, 20-Aug-2001.) |
Ref | Expression |
---|---|
2nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8964 |
. 2
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2 | 1nn 8916 |
. . 3
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3 | peano2nn 8917 |
. . 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 4118 ax-cnex 7890 ax-resscn 7891 ax-1re 7893 ax-addrcl 7896 |
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 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-br 4001 df-iota 5174 df-fv 5220 df-ov 5872 df-inn 8906 df-2 8964 |
This theorem is referenced by: 3nn 9067 2nn0 9179 2z 9267 uz3m2nn 9559 ige2m1fz1 10092 qbtwnre 10240 flhalf 10285 sqeq0 10566 sqeq0d 10635 facavg 10707 bcn2 10725 resqrexlemnm 11008 abs00ap 11052 geo2sum 11503 geo2lim 11505 ege2le3 11660 ef01bndlem 11745 mod2eq0even 11863 mod2eq1n2dvds 11864 sqgcd 12010 3lcm2e6woprm 12066 prm2orodd 12106 3prm 12108 4nprm 12109 isprm5lem 12121 divgcdodd 12123 isevengcd2 12138 3lcm2e6 12140 pw2dvdslemn 12145 pw2dvds 12146 pw2dvdseulemle 12147 oddpwdclemxy 12149 oddpwdclemodd 12152 oddpwdclemdc 12153 oddpwdc 12154 sqpweven 12155 2sqpwodd 12156 pythagtriplem4 12248 oddprmdvds 12332 4sqlem5 12360 4sqlem6 12361 4sqlem10 12365 evenennn 12374 exmidunben 12407 plusgndx 12546 plusgid 12547 plusgslid 12548 grpstrg 12560 grpbaseg 12561 grpplusgg 12562 rngstrg 12569 lmodstrd 12590 topgrpstrd 12615 dsndx 12622 dsid 12623 dsslid 12624 dsndxnn 12625 slotsdifdsndx 12632 dveflem 13847 lgsval 14065 lgsfvalg 14066 lgsfcl2 14067 lgsval2lem 14071 lgsdir2lem2 14090 lgsdir2 14094 2sqlem3 14113 2sqlem8 14119 ex-fl 14126 ex-ceil 14127 redcwlpolemeq1 14451 nconstwlpolem0 14459 |
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