![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > 8nn0 | Structured version Visualization version GIF version |
Description: 8 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
8nn0 | ⊢ 8 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 8nn 11229 | . 2 ⊢ 8 ∈ ℕ | |
2 | 1 | nnnn0i 11338 | 1 ⊢ 8 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2030 8c8 11114 ℕ0cn0 11330 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-8 2032 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 ax-sep 4814 ax-nul 4822 ax-pow 4873 ax-pr 4936 ax-un 6991 ax-1cn 10032 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3or 1055 df-3an 1056 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-eu 2502 df-mo 2503 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-ne 2824 df-ral 2946 df-rex 2947 df-reu 2948 df-rab 2950 df-v 3233 df-sbc 3469 df-csb 3567 df-dif 3610 df-un 3612 df-in 3614 df-ss 3621 df-pss 3623 df-nul 3949 df-if 4120 df-pw 4193 df-sn 4211 df-pr 4213 df-tp 4215 df-op 4217 df-uni 4469 df-iun 4554 df-br 4686 df-opab 4746 df-mpt 4763 df-tr 4786 df-id 5053 df-eprel 5058 df-po 5064 df-so 5065 df-fr 5102 df-we 5104 df-xp 5149 df-rel 5150 df-cnv 5151 df-co 5152 df-dm 5153 df-rn 5154 df-res 5155 df-ima 5156 df-pred 5718 df-ord 5764 df-on 5765 df-lim 5766 df-suc 5767 df-iota 5889 df-fun 5928 df-fn 5929 df-f 5930 df-f1 5931 df-fo 5932 df-f1o 5933 df-fv 5934 df-ov 6693 df-om 7108 df-wrecs 7452 df-recs 7513 df-rdg 7551 df-nn 11059 df-2 11117 df-3 11118 df-4 11119 df-5 11120 df-6 11121 df-7 11122 df-8 11123 df-n0 11331 |
This theorem is referenced by: 8p3e11 11650 8p3e11OLD 11651 8p4e12 11652 8p5e13 11653 8p6e14 11654 8p7e15 11655 8p8e16 11656 9p9e18 11665 6t4e24 11681 7t5e35 11689 8t3e24 11693 8t4e32 11694 8t5e40 11695 8t5e40OLD 11696 8t6e48 11697 8t6e48OLD 11698 8t7e56 11699 8t8e64 11700 9t3e27 11702 9t9e81 11708 2exp16 15844 19prm 15872 prmlem2 15874 37prm 15875 43prm 15876 83prm 15877 139prm 15878 163prm 15879 317prm 15880 631prm 15881 1259lem1 15885 1259lem2 15886 1259lem3 15887 1259lem4 15888 1259lem5 15889 1259prm 15890 2503lem1 15891 2503lem2 15892 2503lem3 15893 2503prm 15894 4001lem1 15895 4001lem2 15896 4001lem3 15897 4001lem4 15898 4001prm 15899 srads 19234 log2ublem3 24720 log2ub 24721 bpos1 25053 2lgslem3a 25166 2lgslem3b 25167 2lgslem3c 25168 2lgslem3d 25169 baseltedgf 25917 ex-exp 27437 hgt750lem 30857 hgt750lem2 30858 tgoldbachgtde 30866 fmtno5lem1 41790 fmtno5lem3 41792 fmtno5lem4 41793 257prm 41798 fmtno4prmfac 41809 fmtno4nprmfac193 41811 fmtno5faclem1 41816 fmtno5faclem3 41818 fmtno5fac 41819 139prmALT 41836 2exp7 41839 127prm 41840 m7prm 41841 2exp11 41842 m11nprm 41843 bgoldbachlt 42026 tgblthelfgott 42028 tgoldbachlt 42029 tgblthelfgottOLD 42034 tgoldbachltOLD 42035 |
Copyright terms: Public domain | W3C validator |