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Mirrors > Home > ILE Home > Th. List > 3bitr4i | Unicode version |
Description: A chained inference from transitive law for logical equivalence. This inference is frequently used to apply a definition to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
3bitr4i.1 |
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3bitr4i.2 |
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3bitr4i.3 |
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Ref | Expression |
---|---|
3bitr4i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3bitr4i.2 |
. 2
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2 | 3bitr4i.1 |
. . 3
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3 | 3bitr4i.3 |
. . 3
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4 | 2, 3 | bitr4i 187 |
. 2
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5 | 1, 4 | bitri 184 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: bibi2d 232 pm4.71 389 pm5.32ri 455 mpan10 474 an31 564 an4 586 or4 771 ordir 817 andir 819 3anrot 983 3orrot 984 3ancoma 985 3orcomb 987 3ioran 993 3anbi123i 1188 3orbi123i 1189 3or6 1323 xorcom 1388 nfbii 1473 19.26-3an 1483 alnex 1499 19.42h 1687 19.42 1688 equsal 1727 equsalv 1793 sb6 1886 eeeanv 1933 sbbi 1959 sbco3xzyz 1973 sbcom2v 1985 sbel2x 1998 sb8eu 2039 sb8mo 2040 sb8euh 2049 eu1 2051 cbvmo 2066 mo3h 2079 sbmo 2085 eqcom 2179 abeq1 2287 cbvabw 2300 cbvab 2301 clelab 2303 nfceqi 2315 sbabel 2346 ralbii2 2487 rexbii2 2488 r2alf 2494 r2exf 2495 nfraldya 2512 nfrexdya 2513 r3al 2521 r19.41 2632 r19.42v 2634 ralcomf 2638 rexcomf 2639 reean 2646 3reeanv 2648 rabid2 2654 rabbi 2655 reubiia 2662 rmobiia 2667 reu5 2690 rmo5 2693 cbvralfw 2695 cbvrexfw 2696 cbvralf 2697 cbvrexf 2698 cbvreu 2703 cbvrmo 2704 cbvralvw 2709 cbvrexvw 2710 vjust 2740 ceqsex3v 2781 ceqsex4v 2782 ceqsex8v 2784 eueq 2910 reu2 2927 reu6 2928 reu3 2929 rmo4 2932 rmo3f 2936 2rmorex 2945 cbvsbcw 2992 cbvsbc 2993 sbccomlem 3039 rmo3 3056 csbcow 3070 csbabg 3120 cbvralcsf 3121 cbvrexcsf 3122 cbvreucsf 3123 eqss 3172 uniiunlem 3246 ssequn1 3307 unss 3311 rexun 3317 ralunb 3318 elin3 3328 incom 3329 inass 3347 ssin 3359 ssddif 3371 unssdif 3372 difin 3374 invdif 3379 indif 3380 indi 3384 symdifxor 3403 disj3 3477 eldifpr 3621 rexsns 3633 reusn 3665 prss 3750 tpss 3760 eluni2 3815 elunirab 3824 uniun 3830 uni0b 3836 unissb 3841 elintrab 3858 ssintrab 3869 intun 3877 intpr 3878 iuncom 3894 iuncom4 3895 iunab 3935 ssiinf 3938 iinab 3950 iunin2 3952 iunun 3967 iunxun 3968 iunxiun 3970 sspwuni 3973 iinpw 3979 cbvdisj 3992 brun 4056 brin 4057 brdif 4058 dftr2 4105 inuni 4157 repizf2lem 4163 unidif0 4169 ssext 4223 pweqb 4225 otth2 4243 opelopabsbALT 4261 eqopab2b 4281 pwin 4284 unisuc 4415 elpwpwel 4477 sucexb 4498 elomssom 4606 xpiundi 4686 xpiundir 4687 poinxp 4697 soinxp 4698 seinxp 4699 inopab 4761 difopab 4762 raliunxp 4770 rexiunxp 4771 iunxpf 4777 cnvco 4814 dmiun 4838 dmuni 4839 dm0rn0 4846 brres 4915 dmres 4930 restidsing 4965 cnvsym 5014 asymref 5016 codir 5019 qfto 5020 cnvopab 5032 cnvdif 5037 rniun 5041 dminss 5045 imainss 5046 cnvcnvsn 5107 resco 5135 imaco 5136 rnco 5137 coiun 5140 coass 5149 ressn 5171 cnviinm 5172 xpcom 5177 funcnv 5279 funcnv3 5280 fncnv 5284 fun11 5285 fnres 5334 dfmpt3 5340 fnopabg 5341 fintm 5403 fin 5404 fores 5449 dff1o3 5469 fun11iun 5484 f11o 5496 f1ompt 5669 fsn 5690 imaiun 5763 isores2 5816 eqoprab2b 5935 opabex3d 6124 opabex3 6125 dfopab2 6192 dfoprab3s 6193 fmpox 6203 tpostpos 6267 dfsmo2 6290 qsid 6602 mapval2 6680 mapsncnv 6697 elixp2 6704 ixpin 6725 xpassen 6832 diffitest 6889 pw1dc0el 6913 supmoti 6994 eqinfti 7021 distrnqg 7388 ltbtwnnq 7417 distrnq0 7460 nqprrnd 7544 ltresr 7840 elznn0nn 9269 xrnemnf 9779 xrnepnf 9780 elioomnf 9970 elxrge0 9980 elfzuzb 10021 fzass4 10064 elfz2nn0 10114 elfzo2 10152 elfzo3 10165 lbfzo0 10183 fzind2 10241 dfrp2 10266 rexfiuz 11000 fisumcom2 11448 prodmodc 11588 fprodcom2fi 11636 infssuzex 11952 infpn2 12459 xpsfrnel 12768 xpscf 12771 islmod 13386 isbasis2g 13584 tgval2 13590 ntreq0 13671 txuni2 13795 isms2 13993 bdceq 14633 |
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