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Mirrors > Home > ILE Home > Th. List > mp3an3 | Unicode version |
Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994.) |
Ref | Expression |
---|---|
mp3an3.1 |
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mp3an3.2 |
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Ref | Expression |
---|---|
mp3an3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mp3an3.1 |
. 2
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2 | mp3an3.2 |
. . 3
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3 | 2 | 3expia 1207 |
. 2
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4 | 1, 3 | mpi 15 |
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 982 |
This theorem is referenced by: mp3an13 1339 mp3an23 1340 mp3anl3 1344 opelxp 4689 funimaexg 5338 ov 6038 ovmpoa 6049 ovmpo 6054 ovtposg 6312 oaword1 6524 th3q 6694 enrefg 6818 f1imaen 6848 mapxpen 6904 pw1fin 6966 xpfi 6986 djucomen 7276 addnnnq0 7509 mulnnnq0 7510 prarloclemcalc 7562 genpelxp 7571 genpprecll 7574 genppreclu 7575 addsrpr 7805 mulsrpr 7806 gt0srpr 7808 mulrid 8016 ltneg 8481 leneg 8484 suble0 8495 div1 8722 nnaddcl 9002 nnmulcl 9003 nnge1 9005 nnsub 9021 2halves 9211 halfaddsub 9216 addltmul 9219 zleltp1 9372 nnaddm1cl 9378 zextlt 9409 peano5uzti 9425 eluzp1p1 9618 uzaddcl 9651 znq 9689 xrre 9886 xrre2 9887 fzshftral 10174 nninfinf 10514 expn1ap0 10620 expadd 10652 expmul 10655 expubnd 10667 sqmul 10672 bernneq 10731 sqrecapd 10748 faclbnd2 10813 faclbnd6 10815 fihashssdif 10889 shftval3 10971 caucvgre 11125 leabs 11218 ltabs 11231 caubnd2 11261 efexp 11825 efival 11875 cos01gt0 11906 odd2np1 12014 halfleoddlt 12035 omoe 12037 opeo 12038 gcdmultiple 12157 sqgcd 12166 nn0seqcvgd 12179 phiprmpw 12360 eulerthlemth 12370 odzcllem 12380 pcelnn 12459 4sqlem3 12528 lsp0 13919 lss0v 13926 zndvds0 14138 ntrin 14292 txuni2 14424 txopn 14433 xblpnfps 14566 xblpnf 14567 bl2in 14571 unirnblps 14590 unirnbl 14591 blpnfctr 14607 plyconst 14891 plyid 14892 sincosq1eq 14974 rpcxpp1 15041 rplogb1 15080 |
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