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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 11468 | . 2 ⊢ 5 ∈ ℕ | |
2 | 1 | nnnn0i 11656 | 1 ⊢ 5 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2107 5c5 11438 ℕ0cn0 11647 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-8 2109 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-13 2334 ax-ext 2754 ax-sep 5019 ax-nul 5027 ax-pow 5079 ax-pr 5140 ax-un 7228 ax-1cn 10332 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-3or 1072 df-3an 1073 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-mo 2551 df-eu 2587 df-clab 2764 df-cleq 2770 df-clel 2774 df-nfc 2921 df-ne 2970 df-ral 3095 df-rex 3096 df-reu 3097 df-rab 3099 df-v 3400 df-sbc 3653 df-csb 3752 df-dif 3795 df-un 3797 df-in 3799 df-ss 3806 df-pss 3808 df-nul 4142 df-if 4308 df-pw 4381 df-sn 4399 df-pr 4401 df-tp 4403 df-op 4405 df-uni 4674 df-iun 4757 df-br 4889 df-opab 4951 df-mpt 4968 df-tr 4990 df-id 5263 df-eprel 5268 df-po 5276 df-so 5277 df-fr 5316 df-we 5318 df-xp 5363 df-rel 5364 df-cnv 5365 df-co 5366 df-dm 5367 df-rn 5368 df-res 5369 df-ima 5370 df-pred 5935 df-ord 5981 df-on 5982 df-lim 5983 df-suc 5984 df-iota 6101 df-fun 6139 df-fn 6140 df-f 6141 df-f1 6142 df-fo 6143 df-f1o 6144 df-fv 6145 df-ov 6927 df-om 7346 df-wrecs 7691 df-recs 7753 df-rdg 7791 df-nn 11380 df-2 11443 df-3 11444 df-4 11445 df-5 11446 df-n0 11648 |
This theorem is referenced by: 6p6e12 11926 7p6e13 11930 8p6e14 11936 8p8e16 11938 9p6e15 11943 9p7e16 11944 5t2e10 11952 5t3e15 11953 5t4e20 11954 5t5e25 11955 6t6e36 11960 7t5e35 11964 7t6e42 11965 8t6e48 11971 8t8e64 11973 9t5e45 11977 9t6e54 11978 9t7e63 11979 dec2dvds 16182 dec5dvds2 16184 2exp8 16206 2exp16 16207 prmlem1 16224 5prm 16225 7prm 16227 11prm 16231 13prm 16232 17prm 16233 19prm 16234 prmlem2 16236 37prm 16237 139prm 16240 163prm 16241 317prm 16242 631prm 16243 1259lem1 16247 1259lem2 16248 1259lem3 16249 1259lem4 16250 1259lem5 16251 1259prm 16252 2503lem1 16253 2503lem2 16254 2503lem3 16255 2503prm 16256 4001lem1 16257 4001lem2 16258 4001lem3 16259 4001lem4 16260 4001prm 16261 ressco 16476 slotsbhcdif 16477 quart1cl 25043 quart1lem 25044 quart1 25045 log2ublem1 25136 log2ublem3 25138 log2ub 25139 log2le1 25140 birthday 25144 ppiublem2 25391 bpos1 25471 bposlem8 25479 ex-fac 27900 threehalves 30199 zlmds 30614 hgt750lemd 31336 hgt750lem2 31340 hgt750leme 31346 kur14lem8 31802 sqn5i 38161 235t711 38167 ex-decpmul 38168 inductionexd 39423 fmtno3 42498 fmtno4 42499 fmtno5lem1 42500 fmtno5lem2 42501 fmtno5lem3 42502 fmtno5lem4 42503 fmtno5 42504 257prm 42508 fmtno4prmfac 42519 fmtno4prmfac193 42520 fmtno4nprmfac193 42521 fmtno5faclem3 42528 flsqrt5 42544 139prmALT 42546 31prm 42547 127prm 42550 2exp11 42552 41prothprmlem2 42570 linevalexample 43213 |
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