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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 11401 | . 2 ⊢ 6 ∈ ℕ | |
2 | 1 | nnnn0i 11512 | 1 ⊢ 6 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2139 6c6 11286 ℕ0cn0 11504 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-8 2141 ax-9 2148 ax-10 2168 ax-11 2183 ax-12 2196 ax-13 2391 ax-ext 2740 ax-sep 4933 ax-nul 4941 ax-pow 4992 ax-pr 5055 ax-un 7115 ax-1cn 10206 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3or 1073 df-3an 1074 df-tru 1635 df-ex 1854 df-nf 1859 df-sb 2047 df-eu 2611 df-mo 2612 df-clab 2747 df-cleq 2753 df-clel 2756 df-nfc 2891 df-ne 2933 df-ral 3055 df-rex 3056 df-reu 3057 df-rab 3059 df-v 3342 df-sbc 3577 df-csb 3675 df-dif 3718 df-un 3720 df-in 3722 df-ss 3729 df-pss 3731 df-nul 4059 df-if 4231 df-pw 4304 df-sn 4322 df-pr 4324 df-tp 4326 df-op 4328 df-uni 4589 df-iun 4674 df-br 4805 df-opab 4865 df-mpt 4882 df-tr 4905 df-id 5174 df-eprel 5179 df-po 5187 df-so 5188 df-fr 5225 df-we 5227 df-xp 5272 df-rel 5273 df-cnv 5274 df-co 5275 df-dm 5276 df-rn 5277 df-res 5278 df-ima 5279 df-pred 5841 df-ord 5887 df-on 5888 df-lim 5889 df-suc 5890 df-iota 6012 df-fun 6051 df-fn 6052 df-f 6053 df-f1 6054 df-fo 6055 df-f1o 6056 df-fv 6057 df-ov 6817 df-om 7232 df-wrecs 7577 df-recs 7638 df-rdg 7676 df-nn 11233 df-2 11291 df-3 11292 df-4 11293 df-5 11294 df-6 11295 df-n0 11505 |
This theorem is referenced by: 6p5e11 11812 6p5e11OLD 11813 6p6e12 11814 7p7e14 11821 8p7e15 11829 9p7e16 11837 9p8e17 11838 6t3e18 11854 6t4e24 11855 6t5e30 11856 6t5e30OLD 11857 6t6e36 11858 6t6e36OLD 11859 7t7e49 11865 8t3e24 11867 8t7e56 11873 8t8e64 11874 9t4e36 11877 9t5e45 11878 9t7e63 11880 9t8e72 11881 6lcm4e12 15551 2exp8 16018 2exp16 16019 2expltfac 16021 19prm 16047 prmlem2 16049 37prm 16050 43prm 16051 139prm 16053 163prm 16054 317prm 16055 631prm 16056 1259lem1 16060 1259lem2 16061 1259lem3 16062 1259lem4 16063 1259lem5 16064 2503lem1 16066 2503lem2 16067 2503lem3 16068 2503prm 16069 4001lem1 16070 4001lem2 16071 4001lem3 16072 4001lem4 16073 4001prm 16074 log2ublem2 24894 log2ublem3 24895 log2ub 24896 log2le1 24897 birthday 24901 bclbnd 25225 bpos1 25228 bposlem8 25236 bposlem9 25237 bpos 25238 ttgval 25975 ttglem 25976 ttgbas 25977 ttgplusg 25978 ttgvsca 25980 eengstr 26080 ex-exp 27639 zlmds 30338 hgt750lemd 31056 hgt750lem 31059 hgt750lem2 31060 kur14lem8 31523 expdiophlem2 38109 wallispi2lem2 40810 fmtno2 41990 fmtno3 41991 fmtno4 41992 fmtno5lem1 41993 fmtno5lem2 41994 fmtno5lem3 41995 fmtno5lem4 41996 fmtno5 41997 257prm 42001 fmtno4prmfac 42012 fmtno4nprmfac193 42014 fmtno5faclem1 42019 fmtno5faclem2 42020 fmtno5faclem3 42021 fmtno5fac 42022 fmtno5nprm 42023 139prmALT 42039 2exp7 42042 127prm 42043 2exp11 42045 m11nprm 42046 |
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