Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 11717 | . 2 ⊢ 5 ∈ ℕ | |
2 | 1 | nnnn0i 11899 | 1 ⊢ 5 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2110 5c5 11689 ℕ0cn0 11891 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2156 ax-12 2172 ax-ext 2793 ax-sep 5196 ax-nul 5203 ax-pow 5259 ax-pr 5322 ax-un 7455 ax-1cn 10589 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3or 1084 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 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 3773 df-csb 3884 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-pss 3954 df-nul 4292 df-if 4468 df-pw 4541 df-sn 4562 df-pr 4564 df-tp 4566 df-op 4568 df-uni 4833 df-iun 4914 df-br 5060 df-opab 5122 df-mpt 5140 df-tr 5166 df-id 5455 df-eprel 5460 df-po 5469 df-so 5470 df-fr 5509 df-we 5511 df-xp 5556 df-rel 5557 df-cnv 5558 df-co 5559 df-dm 5560 df-rn 5561 df-res 5562 df-ima 5563 df-pred 6143 df-ord 6189 df-on 6190 df-lim 6191 df-suc 6192 df-iota 6309 df-fun 6352 df-fn 6353 df-f 6354 df-f1 6355 df-fo 6356 df-f1o 6357 df-fv 6358 df-ov 7153 df-om 7575 df-wrecs 7941 df-recs 8002 df-rdg 8040 df-nn 11633 df-2 11694 df-3 11695 df-4 11696 df-5 11697 df-n0 11892 |
This theorem is referenced by: 6p6e12 12166 7p6e13 12170 8p6e14 12176 8p8e16 12178 9p6e15 12183 9p7e16 12184 5t2e10 12192 5t3e15 12193 5t4e20 12194 5t5e25 12195 6t6e36 12200 7t5e35 12204 7t6e42 12205 8t6e48 12211 8t8e64 12213 9t5e45 12217 9t6e54 12218 9t7e63 12219 dec2dvds 16393 dec5dvds2 16395 2exp8 16417 2exp16 16418 prmlem1 16435 5prm 16436 7prm 16438 11prm 16442 13prm 16443 17prm 16444 19prm 16445 prmlem2 16447 37prm 16448 139prm 16451 163prm 16452 317prm 16453 631prm 16454 1259lem1 16458 1259lem2 16459 1259lem3 16460 1259lem4 16461 1259lem5 16462 1259prm 16463 2503lem1 16464 2503lem2 16465 2503lem3 16466 2503prm 16467 4001lem1 16468 4001lem2 16469 4001lem3 16470 4001lem4 16471 4001prm 16472 ressco 16686 slotsbhcdif 16687 quart1cl 25426 quart1lem 25427 quart1 25428 log2ublem1 25518 log2ublem3 25520 log2ub 25521 log2le1 25522 birthday 25526 ppiublem2 25773 bpos1 25853 bposlem8 25861 ex-fac 28224 threehalves 30586 zlmds 31200 hgt750lemd 31914 hgt750lem2 31918 hgt750leme 31924 kur14lem8 32455 sqn5i 39164 235t711 39170 ex-decpmul 39171 3cubeslem3l 39276 3cubeslem3r 39277 inductionexd 40498 fmtno3 43706 fmtno4 43707 fmtno5lem1 43708 fmtno5lem2 43709 fmtno5lem3 43710 fmtno5lem4 43711 fmtno5 43712 257prm 43716 fmtno4prmfac 43727 fmtno4prmfac193 43728 fmtno4nprmfac193 43729 fmtno5faclem3 43736 flsqrt5 43750 139prmALT 43752 31prm 43753 127prm 43756 2exp11 43758 41prothprmlem2 43776 2exp340mod341 43891 linevalexample 44443 |
Copyright terms: Public domain | W3C validator |