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Mirrors > Home > MPE Home > Th. List > neg1ne0 | Structured version Visualization version GIF version |
Description: -1 is nonzero. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
neg1ne0 | ⊢ -1 ≠ 0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 10811 | . 2 ⊢ 1 ∈ ℂ | |
2 | ax-1ne0 10822 | . 2 ⊢ 1 ≠ 0 | |
3 | 1, 2 | negne0i 11177 | 1 ⊢ -1 ≠ 0 |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2941 0cc0 10753 1c1 10754 -cneg 11087 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2159 ax-12 2176 ax-ext 2709 ax-sep 5206 ax-nul 5213 ax-pow 5272 ax-pr 5336 ax-un 7541 ax-resscn 10810 ax-1cn 10811 ax-icn 10812 ax-addcl 10813 ax-addrcl 10814 ax-mulcl 10815 ax-mulrcl 10816 ax-mulcom 10817 ax-addass 10818 ax-mulass 10819 ax-distr 10820 ax-i2m1 10821 ax-1ne0 10822 ax-1rid 10823 ax-rnegex 10824 ax-rrecex 10825 ax-cnre 10826 ax-pre-lttri 10827 ax-pre-lttrn 10828 ax-pre-ltadd 10829 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-3or 1090 df-3an 1091 df-tru 1546 df-fal 1556 df-ex 1788 df-nf 1792 df-sb 2072 df-mo 2540 df-eu 2569 df-clab 2716 df-cleq 2730 df-clel 2817 df-nfc 2887 df-ne 2942 df-nel 3048 df-ral 3067 df-rex 3068 df-reu 3069 df-rab 3071 df-v 3422 df-sbc 3709 df-csb 3826 df-dif 3883 df-un 3885 df-in 3887 df-ss 3897 df-nul 4252 df-if 4454 df-pw 4529 df-sn 4556 df-pr 4558 df-op 4562 df-uni 4834 df-br 5068 df-opab 5130 df-mpt 5150 df-id 5469 df-po 5482 df-so 5483 df-xp 5571 df-rel 5572 df-cnv 5573 df-co 5574 df-dm 5575 df-rn 5576 df-res 5577 df-ima 5578 df-iota 6355 df-fun 6399 df-fn 6400 df-f 6401 df-f1 6402 df-fo 6403 df-f1o 6404 df-fv 6405 df-riota 7188 df-ov 7234 df-oprab 7235 df-mpo 7236 df-er 8411 df-en 8647 df-dom 8648 df-sdom 8649 df-pnf 10893 df-mnf 10894 df-ltxr 10896 df-sub 11088 df-neg 11089 |
This theorem is referenced by: m1expcl2 13681 m1expeven 13706 iseraltlem2 15270 iseraltlem3 15271 iseralt 15272 m1expo 15960 m1exp1 15961 psgnunilem4 18913 m1expaddsub 18914 psgnuni 18915 cnmsgnsubg 20563 cnmsgngrp 20565 psgninv 20568 iblcnlem1 24709 itgcnlem 24711 dgrsub 25190 coseq00topi 25416 logtayl2 25574 root1eq1 25665 root1cj 25666 cxpeq 25667 angneg 25710 ang180lem1 25716 1cubrlem 25748 atantayl2 25845 basellem2 25988 isnsqf 26041 dchrfi 26160 dchrptlem1 26169 dchrptlem2 26170 lgsne0 26240 lgseisenlem1 26280 lgseisenlem2 26281 lgseisenlem4 26283 lgseisen 26284 lgsquadlem1 26285 lgsquad2lem1 26289 lgsquad3 26292 m1lgs 26293 hvsubcan 29179 hvsubcan2 29180 superpos 30459 sgnnbi 32248 signswch 32276 signstfvcl 32288 fwddifnp1 34230 proot1ex 40757 m1expevenALTV 44800 m1expoddALTV 44801 |
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