Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > 9nn | Structured version Visualization version Unicode version |
Description: 9 is a positive integer. (Contributed by NM, 21-Oct-2012.) |
Ref | Expression |
---|---|
9nn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-9 11086 | . 2 | |
2 | 8nn 11191 | . . 3 | |
3 | peano2nn 11032 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | eqeltri 2697 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 (class class class)co 6650 c1 9937 caddc 9939 cn 11020 c8 11076 c9 11077 |
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 |
This theorem is referenced by: 10nnOLD 11193 9nn0 11316 9p1e10 11496 10nn 11514 3dvdsdec 15054 3dvdsdecOLD 15055 19prm 15825 prmlem2 15827 37prm 15828 43prm 15829 83prm 15830 139prm 15831 163prm 15832 317prm 15833 631prm 15834 1259lem1 15838 1259lem2 15839 1259lem3 15840 1259lem4 15841 1259lem5 15842 2503lem3 15846 tsetndx 16040 tsetid 16041 topgrpstr 16042 resstset 16046 otpsstr 16051 otpsstrOLD 16055 odrngstr 16066 imasvalstr 16112 ipostr 17153 oppgtset 17782 mgptset 18497 sratset 19184 psrvalstr 19363 cnfldstr 19748 eltpsg 20747 indistpsALT 20817 mcubic 24574 log2cnv 24671 log2tlbnd 24672 log2ublem2 24674 log2ub 24676 bposlem7 25015 ex-cnv 27294 ex-dm 27296 ex-gcd 27314 ex-lcm 27315 ex-prmo 27316 hgt750lem2 30730 rmydioph 37581 deccarry 41321 257prm 41473 fmtno4nprmfac193 41486 139prmALT 41511 127prm 41515 wtgoldbnnsum4prm 41690 bgoldbnnsum3prm 41692 bgoldbtbndlem1 41693 tgblthelfgott 41703 tgblthelfgottOLD 41709 |
Copyright terms: Public domain | W3C validator |