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Mirrors > Home > ILE Home > Th. List > renegcld | Unicode version |
Description: Closure law for negative of reals. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
renegcld.1 |
Ref | Expression |
---|---|
renegcld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | renegcld.1 | . 2 | |
2 | renegcl 8180 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2141 cr 7773 cneg 8091 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-setind 4521 ax-resscn 7866 ax-1cn 7867 ax-icn 7869 ax-addcl 7870 ax-addrcl 7871 ax-mulcl 7872 ax-addcom 7874 ax-addass 7876 ax-distr 7878 ax-i2m1 7879 ax-0id 7882 ax-rnegex 7883 ax-cnre 7885 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-ral 2453 df-rex 2454 df-reu 2455 df-rab 2457 df-v 2732 df-sbc 2956 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fv 5206 df-riota 5809 df-ov 5856 df-oprab 5857 df-mpo 5858 df-sub 8092 df-neg 8093 |
This theorem is referenced by: eqord2 8403 possumd 8488 reapmul1 8514 reapneg 8516 apneg 8530 mulext1 8531 recgt0 8766 prodgt0 8768 prodge0 8770 negiso 8871 nnnegz 9215 peano2z 9248 nn0negleid 9280 difgtsumgt 9281 supinfneg 9554 infsupneg 9555 monoord2 10433 recj 10831 reneg 10832 imcj 10839 imneg 10840 cjap 10870 resqrexlemcalc3 10980 resqrexlemgt0 10984 abslt 11052 absle 11053 minmax 11193 mincl 11194 lemininf 11197 ltmininf 11198 bdtri 11203 xrmaxaddlem 11223 xrminrpcl 11237 climge0 11288 cos12dec 11730 absefib 11733 efieq1re 11734 dvdslelemd 11803 infssuzex 11904 zsupssdc 11909 ivthdec 13416 coseq0negpitopi 13551 cosq34lt1 13565 rpabscxpbnd 13653 lgsneg 13719 lgsdilem 13722 |
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