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| 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 12361 | . 2 ⊢ 8 ∈ ℕ | |
| 2 | 1 | nnnn0i 12534 | 1 ⊢ 8 ∈ ℕ0 |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2108 8c8 12327 ℕ0cn0 12526 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pr 5432 ax-un 7755 ax-1cn 11213 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3or 1088 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2540 df-eu 2569 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-ne 2941 df-ral 3062 df-rex 3071 df-reu 3381 df-rab 3437 df-v 3482 df-sbc 3789 df-csb 3900 df-dif 3954 df-un 3956 df-in 3958 df-ss 3968 df-pss 3971 df-nul 4334 df-if 4526 df-pw 4602 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-iun 4993 df-br 5144 df-opab 5206 df-mpt 5226 df-tr 5260 df-id 5578 df-eprel 5584 df-po 5592 df-so 5593 df-fr 5637 df-we 5639 df-xp 5691 df-rel 5692 df-cnv 5693 df-co 5694 df-dm 5695 df-rn 5696 df-res 5697 df-ima 5698 df-pred 6321 df-ord 6387 df-on 6388 df-lim 6389 df-suc 6390 df-iota 6514 df-fun 6563 df-fn 6564 df-f 6565 df-f1 6566 df-fo 6567 df-f1o 6568 df-fv 6569 df-ov 7434 df-om 7888 df-2nd 8015 df-frecs 8306 df-wrecs 8337 df-recs 8411 df-rdg 8450 df-nn 12267 df-2 12329 df-3 12330 df-4 12331 df-5 12332 df-6 12333 df-7 12334 df-8 12335 df-n0 12527 |
| This theorem is referenced by: 8p3e11 12814 8p4e12 12815 8p5e13 12816 8p6e14 12817 8p7e15 12818 8p8e16 12819 9p9e18 12827 6t4e24 12839 7t5e35 12845 8t3e24 12849 8t4e32 12850 8t5e40 12851 8t6e48 12852 8t7e56 12853 8t8e64 12854 9t3e27 12856 9t9e81 12862 2exp11 17127 2exp16 17128 19prm 17155 prmlem2 17157 37prm 17158 43prm 17159 83prm 17160 139prm 17161 163prm 17162 317prm 17163 631prm 17164 1259lem1 17168 1259lem2 17169 1259lem3 17170 1259lem4 17171 1259lem5 17172 1259prm 17173 2503lem1 17174 2503lem2 17175 2503lem3 17176 2503prm 17177 4001lem1 17178 4001lem2 17179 4001lem3 17180 4001lem4 17181 4001prm 17182 slotsdnscsi 17436 sradsOLD 21192 log2ublem3 26991 log2ub 26992 bpos1 27327 2lgslem3a 27440 2lgslem3b 27441 2lgslem3c 27442 2lgslem3d 27443 basendxltedgfndx 29010 baseltedgfOLD 29011 ex-exp 30469 hgt750lem 34666 hgt750lem2 34667 tgoldbachgtde 34675 420gcd8e4 42007 420lcm8e840 42012 lcmineqlem 42053 3exp7 42054 3lexlogpow5ineq1 42055 3lexlogpow5ineq2 42056 3lexlogpow5ineq5 42061 aks4d1p1 42077 235t711 42339 ex-decpmul 42340 sum9cubes 42682 3cubeslem3l 42697 3cubeslem3r 42698 fmtno5lem1 47540 fmtno5lem3 47542 fmtno5lem4 47543 257prm 47548 fmtno4prmfac 47559 fmtno4nprmfac193 47561 fmtno5faclem1 47566 fmtno5faclem3 47568 fmtno5fac 47569 139prmALT 47583 127prm 47586 m7prm 47587 m11nprm 47588 2exp340mod341 47720 8exp8mod9 47723 nfermltl8rev 47729 bgoldbachlt 47800 tgblthelfgott 47802 tgoldbachlt 47803 |
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