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Theorem simp3ll 1244
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3ll ((𝜃𝜏 ∧ ((𝜑𝜓) ∧ 𝜒)) → 𝜑)

Proof of Theorem simp3ll
StepHypRef Expression
1 simpll 765 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜑)
213ad2ant3 1135 1 ((𝜃𝜏 ∧ ((𝜑𝜓) ∧ 𝜒)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1087
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 206  df-an 397  df-3an 1089
This theorem is referenced by:  f1oiso2  7351  omeu  8587  ntrivcvgmul  15852  tsmsxp  23879  tgqioo  24536  ovolunlem2  25239  plyadd  25955  plymul  25956  coeeu  25963  nosupbnd1lem2  27436  noinfbnd1lem2  27451  tghilberti2  28144  btwnconn1lem2  35352  btwnconn1lem3  35353  btwnconn1lem12  35362  athgt  38630  2llnjN  38741  4atlem12b  38785  lncmp  38957  cdlema2N  38966  cdlemc2  39366  cdleme5  39414  cdleme11a  39434  cdleme21ct  39503  cdleme21  39511  cdleme22eALTN  39519  cdleme24  39526  cdleme27cl  39540  cdleme27a  39541  cdleme28  39547  cdleme36a  39634  cdleme42b  39652  cdleme48fvg  39674  cdlemf  39737  cdlemk39  40090  cdlemkid1  40096  dihlsscpre  40408  dihord4  40432  dihord5apre  40436  dihmeetlem20N  40500  mapdh9a  40963  pellex  41875  jm2.27  42049
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