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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 8136 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2128 cr 7731 cneg 8047 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-setind 4496 ax-resscn 7824 ax-1cn 7825 ax-icn 7827 ax-addcl 7828 ax-addrcl 7829 ax-mulcl 7830 ax-addcom 7832 ax-addass 7834 ax-distr 7836 ax-i2m1 7837 ax-0id 7840 ax-rnegex 7841 ax-cnre 7843 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-id 4253 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-iota 5135 df-fun 5172 df-fv 5178 df-riota 5780 df-ov 5827 df-oprab 5828 df-mpo 5829 df-sub 8048 df-neg 8049 |
This theorem is referenced by: eqord2 8359 possumd 8444 reapmul1 8470 reapneg 8472 apneg 8486 mulext1 8487 recgt0 8721 prodgt0 8723 prodge0 8725 negiso 8826 nnnegz 9170 peano2z 9203 supinfneg 9506 infsupneg 9507 monoord2 10376 recj 10767 reneg 10768 imcj 10775 imneg 10776 cjap 10806 resqrexlemcalc3 10916 resqrexlemgt0 10920 abslt 10988 absle 10989 minmax 11129 mincl 11130 lemininf 11133 ltmininf 11134 bdtri 11139 xrmaxaddlem 11157 xrminrpcl 11171 climge0 11222 cos12dec 11664 absefib 11667 efieq1re 11668 dvdslelemd 11735 infssuzex 11836 ivthdec 13033 coseq0negpitopi 13168 cosq34lt1 13182 rpabscxpbnd 13270 |
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