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Mirrors > Home > MPE Home > Th. List > simpli | Structured version Visualization version GIF version |
Description: Inference eliminating a conjunct. (Contributed by NM, 15-Jun-1994.) |
Ref | Expression |
---|---|
simpli.1 | ⊢ (𝜑 ∧ 𝜓) |
Ref | Expression |
---|---|
simpli | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpli.1 | . 2 ⊢ (𝜑 ∧ 𝜓) | |
2 | simpl 472 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 |
This theorem is referenced by: exan 1775 exanOLD 1776 pwundif 4945 tfr2b 7379 rdgfun 7399 oeoa 7564 oeoe 7566 ssdomg 7887 ordtypelem4 8309 ordtypelem6 8311 ordtypelem7 8312 r1limg 8517 rankwflemb 8539 r1elssi 8551 infxpenlem 8719 ackbij2 8948 wunom 9421 mulnzcnopr 10552 negiso 10880 infrenegsup 10883 hashunlei 13072 hashsslei 13073 cos01bnd 14755 cos1bnd 14756 cos2bnd 14757 sin4lt0 14764 egt2lt3 14773 epos 14774 ene1 14777 divalglem5 14958 bitsf1o 15005 gcdaddmlem 15083 strlemor1 15796 zrhpsgnmhm 19749 resubgval 19774 re1r 19778 redvr 19782 refld 19784 txindis 21247 icopnfhmeo 22550 iccpnfcnv 22551 iccpnfhmeo 22552 xrhmeo 22553 cnheiborlem 22561 recvs 22754 qcvs 22755 rrxcph 22988 volf 23104 i1f1 23263 itg11 23264 dvsin 23549 taylthlem2 23932 reefgim 24008 pilem3 24011 pigt2lt4 24012 pire 24014 pipos 24016 sinhalfpi 24024 tan4thpi 24070 sincos3rdpi 24072 circgrp 24102 circsubm 24103 rzgrp 24104 1cubrlem 24368 1cubr 24369 jensenlem2 24514 amgmlem 24516 emcllem6 24527 emcllem7 24528 emgt0 24533 harmonicbnd3 24534 ppiublem1 24727 chtub 24737 bposlem7 24815 lgsdir2lem4 24853 lgsdir2lem5 24854 chebbnd1 24961 mulog2sumlem2 25024 pntpbnd1a 25074 pntpbnd2 25076 pntlemb 25086 pntlemk 25095 qrng0 25110 qrng1 25111 qrngneg 25112 qrngdiv 25113 qabsabv 25118 2trllemE 26083 ex-sqrt 26703 normlem7tALT 27360 hhsssh 27510 shintcli 27572 chintcli 27574 omlsi 27647 qlaxr3i 27879 lnophm 28262 nmcopex 28272 nmcoplb 28273 nmbdfnlbi 28292 nmcfnex 28296 nmcfnlb 28297 hmopidmch 28396 hmopidmpj 28397 chirred 28638 nn0archi 29174 xrge0iifiso 29309 xrge0iifmhm 29313 xrge0pluscn 29314 rezh 29343 qqh0 29356 qqh1 29357 qqhcn 29363 qqhucn 29364 rerrext 29381 cnrrext 29382 mbfmvolf 29655 subfacval3 30425 erdszelem5 30431 erdszelem8 30434 filnetlem3 31545 filnetlem4 31546 bj-genr 31776 bj-genl 31777 bj-genan 31778 pigt3 32572 reheibor 32808 fourierdlem68 39067 fourierdlem77 39076 fourierdlem80 39079 fouriersw 39124 etransclem23 39150 gsumge0cl 39264 abcdta 39741 abcdtb 39742 abcdtc 39743 nabctnabc 39747 zlmodzxzsubm 41930 zlmodzxzldeplem3 42085 ldepsnlinclem1 42088 ldepsnlinclem2 42089 ldepsnlinc 42091 empty-surprise 42337 amgmwlem 42357 amgmlemALT 42358 |
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