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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > sxbrsigalem5 | Structured version Visualization version Unicode version |
Description: First direction for sxbrsiga 29185. (Contributed by Thierry Arnoux, 22-Sep-2017.) (Revised by Thierry Arnoux, 11-Oct-2017.) |
Ref | Expression |
---|---|
sxbrsiga.0 |
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dya2ioc.1 |
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dya2ioc.2 |
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Ref | Expression |
---|---|
sxbrsigalem5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sxbrsiga.0 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | dya2ioc.1 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | dya2ioc.2 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | dya2iocucvr 29179 |
. . . 4
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5 | br2base 29164 |
. . . 4
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6 | 4, 5 | eqtr4i 2496 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | brsigarn 29080 |
. . . . . . 7
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8 | 7 | elexi 3041 |
. . . . . 6
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9 | 8, 8 | mpt2ex 6889 |
. . . . 5
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10 | 9 | rnex 6746 |
. . . 4
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11 | 1, 2 | dya2icobrsiga 29171 |
. . . . . . . . . 10
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12 | 11 | sseli 3414 |
. . . . . . . . 9
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13 | 11 | sseli 3414 |
. . . . . . . . 9
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14 | 12, 13 | anim12i 576 |
. . . . . . . 8
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15 | 14 | anim1i 578 |
. . . . . . 7
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16 | 15 | ssoprab2i 6404 |
. . . . . 6
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17 | df-mpt2 6313 |
. . . . . . 7
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18 | 3, 17 | eqtri 2493 |
. . . . . 6
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19 | xpeq1 4853 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | xpeq2 4854 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 19, 20 | cbvmpt2v 6390 |
. . . . . . 7
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22 | df-mpt2 6313 |
. . . . . . 7
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23 | 21, 22 | eqtri 2493 |
. . . . . 6
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24 | 16, 18, 23 | 3sstr4i 3457 |
. . . . 5
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25 | rnss 5069 |
. . . . 5
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26 | 24, 25 | ax-mp 5 |
. . . 4
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27 | sssigagen2 29042 |
. . . 4
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28 | 10, 26, 27 | mp2an 686 |
. . 3
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29 | sigagenss2 29046 |
. . 3
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30 | 6, 28, 10, 29 | mp3an 1390 |
. 2
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31 | 1, 2, 3 | sxbrsigalem4 29182 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | eqid 2471 |
. . . 4
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33 | 32 | sxval 29086 |
. . 3
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34 | 7, 7, 33 | mp2an 686 |
. 2
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35 | 30, 31, 34 | 3sstr4i 3457 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-rep 4508 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 ax-un 6602 ax-inf2 8164 ax-ac2 8911 ax-cnex 9613 ax-resscn 9614 ax-1cn 9615 ax-icn 9616 ax-addcl 9617 ax-addrcl 9618 ax-mulcl 9619 ax-mulrcl 9620 ax-mulcom 9621 ax-addass 9622 ax-mulass 9623 ax-distr 9624 ax-i2m1 9625 ax-1ne0 9626 ax-1rid 9627 ax-rnegex 9628 ax-rrecex 9629 ax-cnre 9630 ax-pre-lttri 9631 ax-pre-lttrn 9632 ax-pre-ltadd 9633 ax-pre-mulgt0 9634 ax-pre-sup 9635 ax-addf 9636 ax-mulf 9637 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3or 1008 df-3an 1009 df-tru 1455 df-fal 1458 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-nel 2644 df-ral 2761 df-rex 2762 df-reu 2763 df-rmo 2764 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-pss 3406 df-nul 3723 df-if 3873 df-pw 3944 df-sn 3960 df-pr 3962 df-tp 3964 df-op 3966 df-uni 4191 df-int 4227 df-iun 4271 df-iin 4272 df-br 4396 df-opab 4455 df-mpt 4456 df-tr 4491 df-eprel 4750 df-id 4754 df-po 4760 df-so 4761 df-fr 4798 df-se 4799 df-we 4800 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-res 4851 df-ima 4852 df-pred 5387 df-ord 5433 df-on 5434 df-lim 5435 df-suc 5436 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 df-isom 5598 df-riota 6270 df-ov 6311 df-oprab 6312 df-mpt2 6313 df-of 6550 df-om 6712 df-1st 6812 df-2nd 6813 df-supp 6934 df-wrecs 7046 df-recs 7108 df-rdg 7146 df-1o 7200 df-2o 7201 df-oadd 7204 df-omul 7205 df-er 7381 df-map 7492 df-pm 7493 df-ixp 7541 df-en 7588 df-dom 7589 df-sdom 7590 df-fin 7591 df-fsupp 7902 df-fi 7943 df-sup 7974 df-inf 7975 df-oi 8043 df-card 8391 df-acn 8394 df-ac 8565 df-cda 8616 df-pnf 9695 df-mnf 9696 df-xr 9697 df-ltxr 9698 df-le 9699 df-sub 9882 df-neg 9883 df-div 10292 df-nn 10632 df-2 10690 df-3 10691 df-4 10692 df-5 10693 df-6 10694 df-7 10695 df-8 10696 df-9 10697 df-10 10698 df-n0 10894 df-z 10962 df-dec 11075 df-uz 11183 df-q 11288 df-rp 11326 df-xneg 11432 df-xadd 11433 df-xmul 11434 df-ioo 11664 df-ioc 11665 df-ico 11666 df-icc 11667 df-fz 11811 df-fzo 11943 df-fl 12061 df-mod 12130 df-seq 12252 df-exp 12311 df-fac 12498 df-bc 12526 df-hash 12554 df-shft 13207 df-cj 13239 df-re 13240 df-im 13241 df-sqrt 13375 df-abs 13376 df-limsup 13603 df-clim 13629 df-rlim 13630 df-sum 13830 df-ef 14198 df-sin 14200 df-cos 14201 df-pi 14203 df-struct 15201 df-ndx 15202 df-slot 15203 df-base 15204 df-sets 15205 df-ress 15206 df-plusg 15281 df-mulr 15282 df-starv 15283 df-sca 15284 df-vsca 15285 df-ip 15286 df-tset 15287 df-ple 15288 df-ds 15290 df-unif 15291 df-hom 15292 df-cco 15293 df-rest 15399 df-topn 15400 df-0g 15418 df-gsum 15419 df-topgen 15420 df-pt 15421 df-prds 15424 df-xrs 15478 df-qtop 15484 df-imas 15485 df-xps 15488 df-mre 15570 df-mrc 15571 df-acs 15573 df-mgm 16566 df-sgrp 16605 df-mnd 16615 df-submnd 16661 df-mulg 16754 df-cntz 17049 df-cmn 17510 df-psmet 19039 df-xmet 19040 df-met 19041 df-bl 19042 df-mopn 19043 df-fbas 19044 df-fg 19045 df-cnfld 19048 df-refld 19250 df-top 19998 df-bases 19999 df-topon 20000 df-topsp 20001 df-cld 20111 df-ntr 20112 df-cls 20113 df-nei 20191 df-lp 20229 df-perf 20230 df-cn 20320 df-cnp 20321 df-haus 20408 df-cmp 20479 df-tx 20654 df-hmeo 20847 df-fil 20939 df-fm 21031 df-flim 21032 df-flf 21033 df-fcls 21034 df-xms 21413 df-ms 21414 df-tms 21415 df-cncf 21988 df-cfil 22303 df-cmet 22305 df-cms 22381 df-limc 22900 df-dv 22901 df-log 23585 df-cxp 23586 df-logb 23781 df-siga 29004 df-sigagen 29035 df-brsiga 29078 df-sx 29085 |
This theorem is referenced by: sxbrsigalem6 29184 |
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