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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 12350 | . 2 ⊢ 7 ∈ ℕ | |
2 | 1 | nnnn0i 12526 | 1 ⊢ 7 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2099 7c7 12318 ℕ0cn0 12518 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2697 ax-sep 5296 ax-nul 5303 ax-pr 5425 ax-un 7738 ax-1cn 11207 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3or 1085 df-3an 1086 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2529 df-eu 2558 df-clab 2704 df-cleq 2718 df-clel 2803 df-nfc 2878 df-ne 2931 df-ral 3052 df-rex 3061 df-reu 3365 df-rab 3420 df-v 3464 df-sbc 3776 df-csb 3892 df-dif 3949 df-un 3951 df-in 3953 df-ss 3963 df-pss 3966 df-nul 4323 df-if 4524 df-pw 4599 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4906 df-iun 4995 df-br 5146 df-opab 5208 df-mpt 5229 df-tr 5263 df-id 5572 df-eprel 5578 df-po 5586 df-so 5587 df-fr 5629 df-we 5631 df-xp 5680 df-rel 5681 df-cnv 5682 df-co 5683 df-dm 5684 df-rn 5685 df-res 5686 df-ima 5687 df-pred 6304 df-ord 6371 df-on 6372 df-lim 6373 df-suc 6374 df-iota 6498 df-fun 6548 df-fn 6549 df-f 6550 df-f1 6551 df-fo 6552 df-f1o 6553 df-fv 6554 df-ov 7419 df-om 7869 df-2nd 7996 df-frecs 8288 df-wrecs 8319 df-recs 8393 df-rdg 8432 df-nn 12259 df-2 12321 df-3 12322 df-4 12323 df-5 12324 df-6 12325 df-7 12326 df-n0 12519 |
This theorem is referenced by: 7p4e11 12799 7p5e12 12800 7p6e13 12801 7p7e14 12802 8p8e16 12809 9p8e17 12816 9p9e18 12817 7t3e21 12833 7t4e28 12834 7t5e35 12835 7t6e42 12836 7t7e49 12837 8t8e64 12844 9t3e27 12846 9t4e36 12847 9t8e72 12851 9t9e81 12852 7prm 17108 17prm 17114 23prm 17116 prmlem2 17117 37prm 17118 83prm 17120 139prm 17121 163prm 17122 317prm 17123 631prm 17124 1259lem1 17128 1259lem2 17129 1259lem3 17130 1259lem4 17131 1259lem5 17132 1259prm 17133 2503lem1 17134 2503lem2 17135 2503lem3 17136 2503prm 17137 4001lem1 17138 4001lem2 17139 4001lem3 17140 4001lem4 17141 4001prm 17142 quartlem1 26882 quartlem2 26883 log2ublem1 26971 log2ublem3 26973 log2ub 26974 bclbnd 27306 bpos1 27309 slotslnbpsd 28366 ex-prmo 30389 hgt750lemd 34507 hgt750lem 34510 hgt750lem2 34511 hgt750leme 34517 tgoldbachgnn 34518 tgoldbachgtde 34519 tgoldbachgt 34522 60lcm7e420 41722 3exp7 41765 3lexlogpow5ineq1 41766 3lexlogpow5ineq2 41767 3lexlogpow2ineq1 41770 3lexlogpow5ineq5 41772 aks4d1p1 41788 235t711 42032 ex-decpmul 42033 3cubeslem3l 42380 3cubeslem3r 42381 expdiophlem2 42717 resqrtvalex 43349 imsqrtvalex 43350 fmtno5lem2 47162 fmtno5lem4 47164 fmtno5 47165 257prm 47169 fmtno4nprmfac193 47182 fmtno5faclem1 47187 fmtno5faclem2 47188 fmtno5fac 47190 fmtno5nprm 47191 139prmALT 47204 127prm 47207 m11nprm 47209 2exp340mod341 47341 tgoldbach 47425 ackval2012 48115 |
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