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Mirrors > Home > MPE Home > Th. List > 6nn0 | Structured version Visualization version GIF version |
Description: 6 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
6nn0 | ⊢ 6 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6nn 11714 | . 2 ⊢ 6 ∈ ℕ | |
2 | 1 | nnnn0i 11893 | 1 ⊢ 6 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2111 6c6 11684 ℕ0cn0 11885 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pow 5231 ax-pr 5295 ax-un 7441 ax-1cn 10584 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3or 1085 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-mo 2598 df-eu 2629 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ne 2988 df-ral 3111 df-rex 3112 df-reu 3113 df-rab 3115 df-v 3443 df-sbc 3721 df-csb 3829 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-pss 3900 df-nul 4244 df-if 4426 df-pw 4499 df-sn 4526 df-pr 4528 df-tp 4530 df-op 4532 df-uni 4801 df-iun 4883 df-br 5031 df-opab 5093 df-mpt 5111 df-tr 5137 df-id 5425 df-eprel 5430 df-po 5438 df-so 5439 df-fr 5478 df-we 5480 df-xp 5525 df-rel 5526 df-cnv 5527 df-co 5528 df-dm 5529 df-rn 5530 df-res 5531 df-ima 5532 df-pred 6116 df-ord 6162 df-on 6163 df-lim 6164 df-suc 6165 df-iota 6283 df-fun 6326 df-fn 6327 df-f 6328 df-f1 6329 df-fo 6330 df-f1o 6331 df-fv 6332 df-ov 7138 df-om 7561 df-wrecs 7930 df-recs 7991 df-rdg 8029 df-nn 11626 df-2 11688 df-3 11689 df-4 11690 df-5 11691 df-6 11692 df-n0 11886 |
This theorem is referenced by: 6p5e11 12159 6p6e12 12160 7p7e14 12165 8p7e15 12171 9p7e16 12178 9p8e17 12179 6t3e18 12191 6t4e24 12192 6t5e30 12193 6t6e36 12194 7t7e49 12200 8t3e24 12202 8t7e56 12206 8t8e64 12207 9t4e36 12210 9t5e45 12211 9t7e63 12213 9t8e72 12214 6lcm4e12 15950 2exp7 16414 2exp8 16415 2exp16 16416 2expltfac 16418 19prm 16443 prmlem2 16445 37prm 16446 43prm 16447 139prm 16449 163prm 16450 317prm 16451 631prm 16452 1259lem1 16456 1259lem2 16457 1259lem3 16458 1259lem4 16459 1259lem5 16460 2503lem1 16462 2503lem2 16463 2503lem3 16464 2503prm 16465 4001lem1 16466 4001lem2 16467 4001lem3 16468 4001lem4 16469 4001prm 16470 log2ublem2 25533 log2ublem3 25534 log2ub 25535 log2le1 25536 birthday 25540 bclbnd 25864 bpos1 25867 bposlem8 25875 bposlem9 25876 bpos 25877 ttgval 26669 ttglem 26670 ttgbas 26671 ttgplusg 26672 ttgvsca 26674 eengstr 26774 ex-exp 28235 zlmds 31315 hgt750lemd 32029 hgt750lem 32032 hgt750lem2 32033 kur14lem8 32573 420gcd8e4 39294 12lcm5e60 39296 60lcm7e420 39298 lcmineqlem 39340 235t711 39485 ex-decpmul 39486 3cubeslem3l 39627 3cubeslem3r 39628 expdiophlem2 39963 resqrtvalex 40345 imsqrtvalex 40346 wallispi2lem2 42714 fmtno2 44067 fmtno3 44068 fmtno4 44069 fmtno5lem1 44070 fmtno5lem2 44071 fmtno5lem3 44072 fmtno5lem4 44073 fmtno5 44074 257prm 44078 fmtno4prmfac 44089 fmtno4nprmfac193 44091 fmtno5faclem1 44096 fmtno5faclem2 44097 fmtno5faclem3 44098 fmtno5fac 44099 fmtno5nprm 44100 139prmALT 44113 127prm 44116 2exp11 44118 m11nprm 44119 2exp340mod341 44251 8exp8mod9 44254 ackval41 45109 ackval42 45110 |
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