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Mirrors > Home > ILE Home > Th. List > adantrl | Unicode version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 4-May-1994.) (Proof shortened by Wolf Lammen, 24-Nov-2012.) |
Ref | Expression |
---|---|
adant2.1 |
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Ref | Expression |
---|---|
adantrl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 110 |
. 2
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2 | adant2.1 |
. 2
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3 | 1, 2 | sylan2 286 |
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 is referenced by: ad2ant2l 508 ad2ant2rl 511 3ad2antr2 1163 3ad2antr3 1164 xordidc 1399 foco 5449 fvun1 5583 isocnv 5812 isores2 5814 f1oiso2 5828 offval 6090 xp2nd 6167 1stconst 6222 2ndconst 6223 tfrlem9 6320 nnmordi 6517 dom2lem 6772 fundmen 6806 mapen 6846 ssenen 6851 ltsonq 7397 ltexnqq 7407 genprndl 7520 genprndu 7521 ltpopr 7594 ltsopr 7595 ltexprlemm 7599 ltexprlemopl 7600 ltexprlemopu 7602 ltexprlemdisj 7605 ltexprlemfl 7608 ltexprlemfu 7610 mulcmpblnrlemg 7739 cnegexlem2 8133 muladd 8341 eqord1 8440 eqord2 8441 divadddivap 8684 ltmul12a 8817 lemul12b 8818 cju 8918 zextlt 9345 supinfneg 9595 infsupneg 9596 xrre 9820 ixxdisj 9903 iooshf 9952 icodisj 9992 iccshftr 9994 iccshftl 9996 iccdil 9998 icccntr 10000 iccf1o 10004 fzaddel 10059 fzsubel 10060 seq3caopr 10483 expineg2 10529 expsubap 10568 expnbnd 10644 facndiv 10719 hashfacen 10816 fprodeq0 11625 lcmdvds 12079 hashdvds 12221 eulerthlemh 12231 pceu 12295 pcqcl 12306 infpnlem1 12357 mhmpropd 12857 grplcan 12932 grplmulf1o 12944 dfgrp3mlem 12968 mulgfng 12987 mulgsubcl 12997 subsubg 13057 eqger 13083 subsubrg 13366 txlm 13782 blininf 13927 xmeter 13939 xmetresbl 13943 limcimo 14137 |
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