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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 8047 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1481 cr 7643 cneg 7958 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-setind 4460 ax-resscn 7736 ax-1cn 7737 ax-icn 7739 ax-addcl 7740 ax-addrcl 7741 ax-mulcl 7742 ax-addcom 7744 ax-addass 7746 ax-distr 7748 ax-i2m1 7749 ax-0id 7752 ax-rnegex 7753 ax-cnre 7755 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-ral 2422 df-rex 2423 df-reu 2424 df-rab 2426 df-v 2691 df-sbc 2914 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-iota 5096 df-fun 5133 df-fv 5139 df-riota 5738 df-ov 5785 df-oprab 5786 df-mpo 5787 df-sub 7959 df-neg 7960 |
This theorem is referenced by: eqord2 8270 possumd 8355 reapmul1 8381 reapneg 8383 apneg 8397 mulext1 8398 recgt0 8632 prodgt0 8634 prodge0 8636 negiso 8737 nnnegz 9081 peano2z 9114 supinfneg 9417 infsupneg 9418 monoord2 10281 recj 10671 reneg 10672 imcj 10679 imneg 10680 cjap 10710 resqrexlemcalc3 10820 resqrexlemgt0 10824 abslt 10892 absle 10893 minmax 11033 mincl 11034 lemininf 11037 ltmininf 11038 bdtri 11043 xrmaxaddlem 11061 xrminrpcl 11075 climge0 11126 cos12dec 11510 absefib 11513 efieq1re 11514 dvdslelemd 11577 infssuzex 11678 ivthdec 12830 coseq0negpitopi 12965 cosq34lt1 12979 rpabscxpbnd 13067 |
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