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Mirrors > Home > MPE Home > Th. List > sq1 | Structured version Visualization version Unicode version |
Description: The square of 1 is 1. (Contributed by NM, 22-Aug-1999.) |
Ref | Expression |
---|---|
sq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2z 11409 | . 2 | |
2 | 1exp 12889 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wcel 1990 (class class class)co 6650 c1 9937 c2 11070 cz 11377 cexp 12860 |
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-cnex 9992 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-mulcom 10000 ax-addass 10001 ax-mulass 10002 ax-distr 10003 ax-i2m1 10004 ax-1ne0 10005 ax-1rid 10006 ax-rnegex 10007 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 ax-pre-lttrn 10011 ax-pre-ltadd 10012 ax-pre-mulgt0 10013 |
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-nel 2898 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 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-riota 6611 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-om 7066 df-2nd 7169 df-wrecs 7407 df-recs 7468 df-rdg 7506 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-xr 10078 df-ltxr 10079 df-le 10080 df-sub 10268 df-neg 10269 df-div 10685 df-nn 11021 df-2 11079 df-n0 11293 df-z 11378 df-uz 11688 df-seq 12802 df-exp 12861 |
This theorem is referenced by: neg1sqe1 12959 binom21 12980 binom2sub1 12982 sq01 12986 sqrlem1 13983 sqrt1 14012 sinbnd 14910 cosbnd 14911 cos1bnd 14917 cos2bnd 14918 cos01gt0 14921 sqnprm 15414 numdensq 15462 zsqrtelqelz 15466 prmreclem1 15620 prmreclem2 15621 4sqlem13 15661 4sqlem19 15667 odadd 18253 abvneg 18834 gzrngunitlem 19811 gzrngunit 19812 zringunit 19836 sinhalfpilem 24215 cos2pi 24228 tangtx 24257 coskpi 24272 tanregt0 24285 efif1olem3 24290 root1id 24495 root1cj 24497 isosctrlem2 24549 asin1 24621 efiatan2 24644 bndatandm 24656 atans2 24658 wilthlem1 24794 dchrinv 24986 sum2dchr 24999 lgslem1 25022 lgsne0 25060 lgssq 25062 lgssq2 25063 1lgs 25065 lgs1 25066 lgsdinn0 25070 lgsquad2lem2 25110 lgsquad3 25112 2lgsoddprmlem3a 25135 2sqlem9 25152 2sqlem10 25153 2sqlem11 25154 2sqblem 25156 2sqb 25157 mulog2sumlem2 25224 pntlemb 25286 axlowdimlem16 25837 ex-pr 27287 normlem1 27967 kbpj 28815 hstnmoc 29082 hstle1 29085 hst1h 29086 hstle 29089 strlem3a 29111 strlem4 29113 strlem5 29114 jplem1 29127 nn0sqeq1 29513 dvasin 33496 dvacos 33497 areacirclem1 33500 areacirc 33505 cntotbnd 33595 pell1qrge1 37434 pell1qr1 37435 pell1qrgaplem 37437 pell14qrgapw 37440 pellqrex 37443 rmspecsqrtnqOLD 37471 rmspecnonsq 37472 rmspecfund 37474 rmspecpos 37481 stoweidlem1 40218 wallispi2lem2 40289 stirlinglem10 40300 lighneallem2 41523 onetansqsecsq 42502 cotsqcscsq 42503 |
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