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Mirrors > Home > MPE Home > Th. List > 9nn0 | Structured version Visualization version Unicode version |
Description: 9 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
9nn0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9nn 11192 | . 2 | |
2 | 1 | nnnn0i 11300 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 c9 11077 cn0 11292 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-1cn 9994 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-om 7066 df-wrecs 7407 df-recs 7468 df-rdg 7506 df-nn 11021 df-2 11079 df-3 11080 df-4 11081 df-5 11082 df-6 11083 df-7 11084 df-8 11085 df-9 11086 df-n0 11293 |
This theorem is referenced by: deccl 11512 le9lt10 11529 declecOLD 11544 decsucc 11550 decsuccOLD 11551 9p2e11 11619 9p2e11OLD 11620 9p3e12 11621 9p4e13 11622 9p5e14 11623 9p6e15 11624 9p7e16 11625 9p8e17 11626 9p9e18 11627 9t3e27 11664 9t4e36 11665 9t5e45 11666 9t6e54 11667 9t7e63 11668 9t8e72 11669 9t9e81 11670 sq10e99m1 13049 sq10e99m1OLD 13052 3dvds2dec 15056 3dvds2decOLD 15057 2exp8 15796 19prm 15825 prmlem2 15827 37prm 15828 83prm 15830 139prm 15831 163prm 15832 317prm 15833 631prm 15834 1259lem1 15838 1259lem2 15839 1259lem3 15840 1259lem4 15841 1259lem5 15842 1259prm 15843 2503lem1 15844 2503lem2 15845 2503lem3 15846 2503prm 15847 4001lem1 15848 4001lem2 15849 4001lem3 15850 4001lem4 15851 cnfldfun 19758 tuslem 22071 setsmsds 22281 tnglem 22444 tngds 22452 log2ublem3 24675 log2ub 24676 bposlem8 25016 dp2lt10 29591 1mhdrd 29624 hgt750lem2 30730 hgt750leme 30736 kur14lem8 31195 fmtno5lem1 41465 fmtno5lem3 41467 fmtno5lem4 41468 fmtno5 41469 257prm 41473 fmtno4prmfac 41484 fmtno4prmfac193 41485 fmtno4nprmfac193 41486 fmtno5fac 41494 139prmALT 41511 127prm 41515 m11nprm 41518 tgblthelfgott 41703 tgoldbachlt 41704 tgblthelfgottOLD 41709 tgoldbachltOLD 41710 |
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