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Theorem simp3rl 1310
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3rl ((𝜃𝜏 ∧ (𝜒 ∧ (𝜑𝜓))) → 𝜑)

Proof of Theorem simp3rl
StepHypRef Expression
1 simprl 811 . 2 ((𝜒 ∧ (𝜑𝜓)) → 𝜑)
213ad2ant3 1129 1 ((𝜃𝜏 ∧ (𝜒 ∧ (𝜑𝜓))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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 197  df-an 385  df-3an 1074
This theorem is referenced by:  omeu  7826  hashbclem  13420  ntrivcvgmul  14825  tsmsxp  22151  tgqioo  22796  ovolunlem2  23458  plyadd  24164  plymul  24165  coeeu  24172  tghilberti2  25724  cvmlift2lem10  31593  nosupbnd1lem2  32153  btwnconn1lem1  32492  btwnconn1lem2  32493  btwnconn1lem12  32503  lplnexllnN  35345  2llnjN  35348  4atlem12b  35392  lplncvrlvol2  35396  lncmp  35564  cdlema2N  35573  cdlemc2  35974  cdleme11a  36042  cdleme22eALTN  36127  cdleme24  36134  cdleme27a  36149  cdleme27N  36151  cdleme28  36155  cdlemefs29bpre0N  36198  cdlemefs29bpre1N  36199  cdlemefs29cpre1N  36200  cdlemefs29clN  36201  cdlemefs32fvaN  36204  cdlemefs32fva1  36205  cdleme36m  36243  cdleme39a  36247  cdleme17d3  36278  cdleme50trn2  36333  cdlemg36  36496  cdlemj3  36605  cdlemkfid1N  36703  cdlemkid1  36704  cdlemk19ylem  36712  cdlemk19xlem  36724  dihlsscpre  37017  dihord4  37041  dihatlat  37117  mapdh9a  37573  jm2.27  38069
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