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Mirrors > Home > MPE Home > Th. List > 5nn | Structured version Visualization version Unicode version |
Description: 5 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
5nn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-5 11082 | . 2 | |
2 | 4nn 11187 | . . 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 c4 11072 c5 11073 |
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 |
This theorem is referenced by: 6nn 11189 5nn0 11312 prm23ge5 15520 dec5dvds 15768 dec5nprm 15770 dec2nprm 15771 5prm 15815 10nprm 15820 10nprmOLD 15821 23prm 15826 prmlem2 15827 43prm 15829 83prm 15830 317prm 15833 prmo5 15836 scandx 16013 scaid 16014 lmodstr 16017 ipsstr 16024 resssca 16031 ccondx 16076 ccoid 16077 ressco 16079 slotsbhcdif 16080 prdsvalstr 16113 oppchomfval 16374 oppcbas 16378 rescco 16492 catstr 16617 lt6abl 18296 mgpsca 18496 psrvalstr 19363 opsrsca 19483 tngsca 22449 log2ublem1 24673 log2ublem2 24674 log2ub 24676 birthday 24681 ppiublem1 24927 ppiublem2 24928 ppiub 24929 bclbnd 25005 bposlem3 25011 bposlem4 25012 bposlem5 25013 bposlem6 25014 bposlem8 25016 bposlem9 25017 lgsdir2lem3 25052 ex-eprel 27290 ex-xp 27293 fib6 30468 hgt750lem2 30730 hgt750leme 30736 rmydioph 37581 expdiophlem2 37589 algstr 37747 inductionexd 38453 257prm 41473 fmtno4prmfac193 41485 31prm 41512 41prothprm 41536 gbowge7 41651 gbege6 41653 stgoldbwt 41664 sbgoldbwt 41665 sbgoldbm 41672 sbgoldbo 41675 nnsum3primesle9 41682 |
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