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Mirrors > Home > MPE Home > Th. List > negsubdi2d | Structured version Visualization version Unicode version |
Description: Distribution of negative over subtraction. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
negidd.1 | |
pncand.2 |
Ref | Expression |
---|---|
negsubdi2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidd.1 | . 2 | |
2 | pncand.2 | . 2 | |
3 | negsubdi2 10340 | . 2 | |
4 | 1, 2, 3 | syl2anc 693 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 (class class class)co 6650 cc 9934 cmin 10266 cneg 10267 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-mulcom 10000 ax-addass 10001 ax-mulass 10002 ax-distr 10003 ax-i2m1 10004 ax-1ne0 10005 ax-1rid 10006 ax-rnegex 10007 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 ax-pre-lttrn 10011 ax-pre-ltadd 10012 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-po 5035 df-so 5036 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-ltxr 10079 df-sub 10268 df-neg 10269 |
This theorem is referenced by: cjneg 13887 icodiamlt 14174 geo2sum2 14605 bpoly3 14789 sinneg 14876 sinhval 14884 vitalilem1 23376 vitalilem1OLD 23377 vitalilem2 23378 itgneg 23570 dvrec 23718 dvferm2lem 23749 dvfsumge 23785 dvfsumlem2 23790 dvfsum2 23797 ftc1lem5 23803 ftc2ditg 23809 plyeq0lem 23966 efif1olem2 24289 ang180 24544 isosctrlem3 24550 isosctr 24551 angpieqvdlem 24555 chordthmlem 24559 mcubic 24574 quart1lem 24582 quartlem1 24584 atanneg 24634 atancj 24637 efiatan 24639 atanlogsub 24643 efiatan2 24644 2efiatan 24645 atantan 24650 atanbndlem 24652 pntrsumo1 25254 pntrlog2bndlem2 25267 pntrlog2bndlem4 25269 pntibndlem2 25280 brbtwn2 25785 colinearalglem4 25789 axsegconlem9 25805 dipcj 27569 bcm1n 29554 signsplypnf 30627 fsum2dsub 30685 dnibndlem11 32478 itg2addnclem3 33463 itg2gt0cn 33465 congsym 37535 cvgdvgrat 38512 negsubdi3d 39506 lptre2pt 39872 liminflimsupclim 40039 stoweidlem13 40230 dirkertrigeqlem2 40316 fourierdlem26 40350 fourierdlem89 40412 fourierdlem90 40413 fourierdlem91 40414 fourierdlem107 40430 etransclem23 40474 sharhght 41054 sigaradd 41055 cevathlem2 41057 fmtnorec3 41460 |
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