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Mirrors > Home > MPE Home > Th. List > cjcld | Structured version Visualization version Unicode version |
Description: Closure law for complex conjugate. (Contributed by Mario Carneiro, 29-May-2016.) |
Ref | Expression |
---|---|
recld.1 |
Ref | Expression |
---|---|
cjcld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | recld.1 | . 2 | |
2 | cjcl 13845 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 cfv 5888 cc 9934 ccj 13836 |
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 ax-pre-mulgt0 10013 |
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-rmo 2920 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-xr 10078 df-ltxr 10079 df-le 10080 df-sub 10268 df-neg 10269 df-div 10685 df-cj 13839 |
This theorem is referenced by: absrpcl 14028 absmul 14034 abstri 14070 abs1m 14075 abslem2 14079 sqreulem 14099 gzcjcl 15640 mul4sqlem 15657 gzrngunit 19812 cphipipcj 23000 cphassr 23012 cph2ass 23013 tchcphlem2 23035 pjthlem1 23208 itgabs 23601 dvcj 23713 dvmptre 23732 dvmptim 23733 tanregt0 24285 logcj 24352 cosargd 24354 root1cj 24497 lawcoslem1 24545 isosctrlem2 24549 asinlem3 24598 atandmcj 24636 atancj 24637 sum2dchr 24999 rpvmasum2 25201 dchrisum0re 25202 pjhthlem1 28250 riesz3i 28921 itgabsnc 33479 ftc1cnnclem 33483 ftc2nc 33494 sigarim 41040 sigarac 41041 sigaraf 41042 sigarmf 41043 sigarls 41046 sigardiv 41050 sharhght 41054 |
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