Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > addsubd | Structured version Visualization version Unicode version |
Description: Law for subtraction and addition. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
negidd.1 | |
pncand.2 | |
subaddd.3 |
Ref | Expression |
---|---|
addsubd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidd.1 | . 2 | |
2 | pncand.2 | . 2 | |
3 | subaddd.3 | . 2 | |
4 | addsub 10292 | . 2 | |
5 | 1, 2, 3, 4 | syl3anc 1326 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 (class class class)co 6650 cc 9934 caddc 9939 cmin 10266 |
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 |
This theorem is referenced by: lesub2 10523 fzoshftral 12585 modadd1 12707 discr 13001 bcp1n 13103 bcpasc 13108 revccat 13515 crre 13854 isercoll2 14399 binomlem 14561 climcndslem1 14581 binomfallfaclem2 14771 pythagtriplem14 15533 vdwlem6 15690 gsumccat 17378 srgbinomlem3 18542 itgcnlem 23556 dvcvx 23783 dvfsumlem1 23789 dvfsumlem2 23790 plymullem1 23970 aaliou3lem2 24098 abelthlem2 24186 tangtx 24257 loglesqrt 24499 dcubic1 24572 quart1lem 24582 quartlem1 24584 basellem3 24809 basellem5 24811 chtub 24937 logfaclbnd 24947 bcp1ctr 25004 lgsquad2lem1 25109 2lgslem3b 25122 selberglem1 25234 selberg3 25248 selbergr 25257 selberg3r 25258 pntlemf 25294 pntlemo 25296 brbtwn2 25785 colinearalglem1 25786 colinearalglem2 25787 crctcsh 26716 clwwlksel 26914 numclwwlkovf2exlem1 27211 ltesubnnd 29568 ballotlemfp1 30553 subfacp1lem6 31167 fwddifnp1 32272 poimirlem25 33434 poimirlem26 33435 jm2.24nn 37526 jm2.18 37555 jm2.25 37566 dvnmul 40158 fourierdlem4 40328 fourierdlem26 40350 fourierdlem42 40366 vonicclem1 40897 cnambpcma 41309 cnapbmcpd 41310 fmtnorec4 41461 ltsubaddb 42304 ltsubadd2b 42306 |
Copyright terms: Public domain | W3C validator |