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Mirrors > Home > MPE Home > Th. List > 5nn0 | Structured version Visualization version GIF version |
Description: 5 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
5nn0 | ⊢ 5 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 5nn 11712 | . 2 ⊢ 5 ∈ ℕ | |
2 | 1 | nnnn0i 11894 | 1 ⊢ 5 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2105 5c5 11684 ℕ0cn0 11886 |
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 2793 ax-sep 5195 ax-nul 5202 ax-pow 5258 ax-pr 5321 ax-un 7450 ax-1cn 10584 |
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 2618 df-eu 2650 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ne 3017 df-ral 3143 df-rex 3144 df-reu 3145 df-rab 3147 df-v 3497 df-sbc 3772 df-csb 3883 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-pss 3953 df-nul 4291 df-if 4466 df-pw 4539 df-sn 4560 df-pr 4562 df-tp 4564 df-op 4566 df-uni 4833 df-iun 4914 df-br 5059 df-opab 5121 df-mpt 5139 df-tr 5165 df-id 5454 df-eprel 5459 df-po 5468 df-so 5469 df-fr 5508 df-we 5510 df-xp 5555 df-rel 5556 df-cnv 5557 df-co 5558 df-dm 5559 df-rn 5560 df-res 5561 df-ima 5562 df-pred 6142 df-ord 6188 df-on 6189 df-lim 6190 df-suc 6191 df-iota 6308 df-fun 6351 df-fn 6352 df-f 6353 df-f1 6354 df-fo 6355 df-f1o 6356 df-fv 6357 df-ov 7148 df-om 7569 df-wrecs 7938 df-recs 7999 df-rdg 8037 df-nn 11628 df-2 11689 df-3 11690 df-4 11691 df-5 11692 df-n0 11887 |
This theorem is referenced by: 6p6e12 12161 7p6e13 12165 8p6e14 12171 8p8e16 12173 9p6e15 12178 9p7e16 12179 5t2e10 12187 5t3e15 12188 5t4e20 12189 5t5e25 12190 6t6e36 12195 7t5e35 12199 7t6e42 12200 8t6e48 12206 8t8e64 12208 9t5e45 12212 9t6e54 12213 9t7e63 12214 dec2dvds 16389 dec5dvds2 16391 2exp8 16413 2exp16 16414 prmlem1 16431 5prm 16432 7prm 16434 11prm 16438 13prm 16439 17prm 16440 19prm 16441 prmlem2 16443 37prm 16444 139prm 16447 163prm 16448 317prm 16449 631prm 16450 1259lem1 16454 1259lem2 16455 1259lem3 16456 1259lem4 16457 1259lem5 16458 1259prm 16459 2503lem1 16460 2503lem2 16461 2503lem3 16462 2503prm 16463 4001lem1 16464 4001lem2 16465 4001lem3 16466 4001lem4 16467 4001prm 16468 ressco 16682 slotsbhcdif 16683 quart1cl 25359 quart1lem 25360 quart1 25361 log2ublem1 25452 log2ublem3 25454 log2ub 25455 log2le1 25456 birthday 25460 ppiublem2 25707 bpos1 25787 bposlem8 25795 ex-fac 28158 threehalves 30519 zlmds 31105 hgt750lemd 31819 hgt750lem2 31823 hgt750leme 31829 kur14lem8 32358 sqn5i 39051 235t711 39057 ex-decpmul 39058 3cubeslem3l 39163 3cubeslem3r 39164 inductionexd 40385 fmtno3 43560 fmtno4 43561 fmtno5lem1 43562 fmtno5lem2 43563 fmtno5lem3 43564 fmtno5lem4 43565 fmtno5 43566 257prm 43570 fmtno4prmfac 43581 fmtno4prmfac193 43582 fmtno4nprmfac193 43583 fmtno5faclem3 43590 flsqrt5 43604 139prmALT 43606 31prm 43607 127prm 43610 2exp11 43612 41prothprmlem2 43630 2exp340mod341 43745 linevalexample 44348 |
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