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Mirrors > Home > ILE Home > Th. List > 3expa | Unicode version |
Description: Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.) |
Ref | Expression |
---|---|
3exp.1 |
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Ref | Expression |
---|---|
3expa |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3exp.1 |
. . 3
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2 | 1 | 3exp 1202 |
. 2
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3 | 2 | imp31 256 |
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 df-3an 980 |
This theorem is referenced by: ad4ant123 1215 ad4ant124 1216 ad4ant134 1217 ad4ant234 1218 3anidm23 1297 mp3an2 1325 mpd3an3 1338 rgen3 2564 moi2 2919 sbc3ie 3037 preq12bg 3774 issod 4320 wepo 4360 reuhypd 4472 funimass4 5567 fvtp1g 5725 f1imass 5775 fcof1o 5790 f1ofveu 5863 f1ocnvfv3 5864 acexmid 5874 2ndrn 6184 frecrdg 6409 oawordriexmid 6471 mapxpen 6848 findcard 6888 findcard2 6889 findcard2s 6890 ltapig 7337 ltanqi 7401 ltmnqi 7402 lt2addnq 7403 lt2mulnq 7404 prarloclemcalc 7501 genpassl 7523 genpassu 7524 prmuloc 7565 ltexprlemm 7599 ltexprlemfl 7608 ltexprlemfu 7610 lteupri 7616 ltaprg 7618 mul4 8089 add4 8118 cnegexlem2 8133 cnegexlem3 8134 2addsub 8171 addsubeq4 8172 muladd 8341 ltleadd 8403 reapmul1 8552 apreim 8560 receuap 8626 p1le 8806 lemul12b 8818 lbinf 8905 zdiv 9341 fzind 9368 fnn0ind 9369 uzss 9548 qmulcl 9637 qreccl 9642 xrlttr 9795 xaddass 9869 icc0r 9926 iooshf 9952 elfz5 10017 elfz0fzfz0 10126 fzind2 10239 ioo0 10260 ico0 10262 ioc0 10263 expnegap0 10528 expineg2 10529 mulexpzap 10560 expsubap 10568 expnbnd 10644 facndiv 10719 bccmpl 10734 bcval5 10743 bcpasc 10746 crim 10867 climshftlemg 11310 2sumeq2dv 11379 hash2iun 11487 2cprodeq2dv 11576 dvdsval3 11798 dvdsnegb 11815 muldvds1 11823 muldvds2 11824 dvdscmul 11825 dvdsmulc 11826 dvds2ln 11831 divalgb 11930 ndvdssub 11935 gcddiv 12020 rpexp1i 12154 phiprmpw 12222 hashgcdeq 12239 pythagtriplem1 12265 pockthg 12355 infpnlem1 12357 4sqlem3 12388 imasaddfnlemg 12735 mndpfo 12839 grplmulf1o 12944 grplactcnv 12972 mulgnn0subcl 12996 mulgsubcl 12997 mulgdir 13015 issubg2m 13049 issubgrpd2 13050 nmzsubg 13070 eqgen 13086 srglmhm 13176 srgrmhm 13177 oppr1g 13252 dvdsrcl2 13268 crngunit 13280 subrgugrp 13361 subsubrg 13366 islmod 13381 lmodvsdir 13402 lmodvsass 13403 innei 13666 iscnp4 13721 cnpnei 13722 cnnei 13735 cnconst 13737 ismeti 13849 isxmet2d 13851 elbl2ps 13895 elbl2 13896 xblpnfps 13901 xblpnf 13902 xblm 13920 blininf 13927 blssexps 13932 blssex 13933 blsscls2 13996 metss 13997 metrest 14009 metcn 14017 divcnap 14058 cdivcncfap 14090 lgslem4 14407 lgscllem 14411 lgsneg1 14429 lgsne0 14442 |
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