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Mirrors > Home > MPE Home > Th. List > 4ne0 | Structured version Visualization version Unicode version |
Description: The number 4 is nonzero. (Contributed by David A. Wheeler, 5-Dec-2018.) |
Ref | Expression |
---|---|
4ne0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4re 11097 | . 2 | |
2 | 4pos 11116 | . 2 | |
3 | 1, 2 | gt0ne0ii 10564 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wne 2794 cc0 9936 c4 11072 |
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-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-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-po 5035 df-so 5036 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-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-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-2 11079 df-3 11080 df-4 11081 |
This theorem is referenced by: 8th4div3 11252 div4p1lem1div2 11287 fldiv4p1lem1div2 12636 fldiv4lem1div2uz2 12637 fldiv4lem1div2 12638 discr 13001 sqoddm1div8 13028 4bc2eq6 13116 bpoly3 14789 bpoly4 14790 flodddiv4 15137 flodddiv4lt 15139 flodddiv4t2lthalf 15140 6lcm4e12 15329 cphipval2 23040 4cphipval2 23041 minveclem3 23200 uniioombl 23357 sincos4thpi 24265 sincos6thpi 24267 heron 24565 quad2 24566 dcubic 24573 mcubic 24574 cubic 24576 dquartlem1 24578 dquartlem2 24579 dquart 24580 quart1cl 24581 quart1lem 24582 quart1 24583 quartlem4 24587 quart 24588 log2tlbnd 24672 bclbnd 25005 bposlem7 25015 bposlem8 25016 bposlem9 25017 gausslemma2dlem0d 25084 gausslemma2dlem3 25093 gausslemma2dlem4 25094 gausslemma2dlem5 25096 m1lgs 25113 2lgslem1a2 25115 2lgslem1 25119 2lgslem2 25120 2lgslem3a 25121 2lgslem3b 25122 2lgslem3c 25123 2lgslem3d 25124 pntibndlem2 25280 4ipval2 27563 ipidsq 27565 dipcl 27567 dipcj 27569 dip0r 27572 dipcn 27575 ip1ilem 27681 ipasslem10 27694 polid2i 28014 lnopeq0i 28866 lnophmlem2 28876 quad3 31564 limclner 39883 stoweid 40280 wallispi2lem1 40288 stirlinglem3 40293 stirlinglem12 40302 stirlinglem13 40303 fouriersw 40448 |
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