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| Description: A negative is a set. (Contributed by NM, 4-Apr-2005.) | 
| Ref | Expression | 
|---|---|
| negex | ⊢ -𝐴 ∈ V | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-neg 11495 | . 2 ⊢ -𝐴 = (0 − 𝐴) | |
| 2 | 1 | ovexi 7465 | 1 ⊢ -𝐴 ∈ V | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∈ wcel 2108 Vcvv 3480 0cc0 11155 − cmin 11492 -cneg 11493 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-nul 5306 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-ne 2941 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-sn 4627 df-pr 4629 df-uni 4908 df-iota 6514 df-fv 6569 df-ov 7434 df-neg 11495 | 
| This theorem is referenced by: negiso 12248 infrenegsup 12251 xnegex 13250 ceilval 13878 monoord2 14074 m1expcl2 14126 sgnval 15127 infcvgaux1i 15893 infcvgaux2i 15894 cnmsgnsubg 21595 evth2 24992 ivth2 25490 mbfinf 25700 mbfi1flimlem 25757 i1fibl 25843 ditgex 25887 dvrec 25993 dvmptsub 26005 dvexp3 26016 rolle 26028 dvlipcn 26033 dvivth 26049 lhop2 26054 dvfsumge 26062 ftc2 26085 plyremlem 26346 advlogexp 26697 logtayl 26702 logccv 26705 dvatan 26978 amgmlem 27033 emcllem7 27045 basellem9 27132 addsqnreup 27487 axlowdimlem7 28963 axlowdimlem8 28964 axlowdimlem9 28965 axlowdimlem13 28969 sgnsval 33181 sgnsf 33182 xrge0iifcv 33933 xrge0iifiso 33934 xrge0iifhom 33936 sgncl 34541 dvtan 37677 ftc1anclem5 37704 ftc1anclem6 37705 ftc2nc 37709 areacirclem1 37715 readvrec 42392 monotoddzzfi 42954 monotoddzz 42955 oddcomabszz 42956 rngunsnply 43181 infnsuprnmpt 45257 liminfltlem 45819 dvcosax 45941 itgsin0pilem1 45965 fourierdlem41 46163 fourierdlem48 46169 fourierdlem102 46223 fourierdlem114 46235 fourierswlem 46245 hoicvr 46563 hoicvrrex 46571 smfliminflem 46845 zlmodzxzldeplem3 48419 amgmwlem 49321 | 
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