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Mirrors > Home > MPE Home > Th. List > 7nn0 | Structured version Visualization version GIF version |
Description: 7 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
7nn0 | ⊢ 7 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 7nn 11717 | . 2 ⊢ 7 ∈ ℕ | |
2 | 1 | nnnn0i 11893 | 1 ⊢ 7 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2105 7c7 11685 ℕ0cn0 11885 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pow 5257 ax-pr 5320 ax-un 7450 ax-1cn 10583 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3or 1080 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ne 3014 df-ral 3140 df-rex 3141 df-reu 3142 df-rab 3144 df-v 3494 df-sbc 3770 df-csb 3881 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-pss 3951 df-nul 4289 df-if 4464 df-pw 4537 df-sn 4558 df-pr 4560 df-tp 4562 df-op 4564 df-uni 4831 df-iun 4912 df-br 5058 df-opab 5120 df-mpt 5138 df-tr 5164 df-id 5453 df-eprel 5458 df-po 5467 df-so 5468 df-fr 5507 df-we 5509 df-xp 5554 df-rel 5555 df-cnv 5556 df-co 5557 df-dm 5558 df-rn 5559 df-res 5560 df-ima 5561 df-pred 6141 df-ord 6187 df-on 6188 df-lim 6189 df-suc 6190 df-iota 6307 df-fun 6350 df-fn 6351 df-f 6352 df-f1 6353 df-fo 6354 df-f1o 6355 df-fv 6356 df-ov 7148 df-om 7570 df-wrecs 7936 df-recs 7997 df-rdg 8035 df-nn 11627 df-2 11688 df-3 11689 df-4 11690 df-5 11691 df-6 11692 df-7 11693 df-n0 11886 |
This theorem is referenced by: 7p4e11 12162 7p5e12 12163 7p6e13 12164 7p7e14 12165 8p8e16 12172 9p8e17 12179 9p9e18 12180 7t3e21 12196 7t4e28 12197 7t5e35 12198 7t6e42 12199 7t7e49 12200 8t8e64 12207 9t3e27 12209 9t4e36 12210 9t8e72 12214 9t9e81 12215 7prm 16432 17prm 16438 23prm 16440 prmlem2 16441 37prm 16442 83prm 16444 139prm 16445 163prm 16446 317prm 16447 631prm 16448 1259lem1 16452 1259lem2 16453 1259lem3 16454 1259lem4 16455 1259lem5 16456 1259prm 16457 2503lem1 16458 2503lem2 16459 2503lem3 16460 2503prm 16461 4001lem1 16462 4001lem2 16463 4001lem3 16464 4001lem4 16465 4001prm 16466 quartlem1 25362 quartlem2 25363 log2ublem1 25451 log2ublem3 25453 log2ub 25454 bclbnd 25783 bpos1 25786 ex-prmo 28165 hgt750lemd 31818 hgt750lem 31821 hgt750lem2 31822 hgt750leme 31828 tgoldbachgnn 31829 tgoldbachgtde 31830 tgoldbachgt 31833 235t711 39055 ex-decpmul 39056 3cubeslem3l 39161 3cubeslem3r 39162 expdiophlem2 39497 fmtno5lem2 43593 fmtno5lem4 43595 fmtno5 43596 257prm 43600 fmtno4nprmfac193 43613 fmtno5faclem1 43618 fmtno5faclem2 43619 fmtno5fac 43621 fmtno5nprm 43622 139prmALT 43636 127prm 43640 m11nprm 43643 2exp340mod341 43775 tgoldbach 43859 |
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