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Theorem simpr2r 1234
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr2r ((𝜏 ∧ (𝜒 ∧ (𝜑𝜓) ∧ 𝜃)) → 𝜓)

Proof of Theorem simpr2r
StepHypRef Expression
1 simprr 772 . 2 ((𝜏 ∧ (𝜑𝜓)) → 𝜓)
213ad2antr2 1190 1 ((𝜏 ∧ (𝜒 ∧ (𝜑𝜓) ∧ 𝜃)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  w3a 1088
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 398  df-3an 1090
This theorem is referenced by:  poxp2  8076  poxp3  8083  frrlem8  8225  ttrcltr  9657  ttrclss  9661  rnttrcl  9663  ttrclselem2  9667  oppccatid  17606  subccatid  17737  setccatid  17975  catccatid  17997  estrccatid  18024  xpccatid  18081  gsmsymgreqlem1  19217  kerf1ghm  20184  ax5seg  27929  3pthdlem1  29150  segconeq  34641  ifscgr  34675  brofs2  34708  brifs2  34709  idinside  34715  btwnconn1lem8  34725  btwnconn1lem11  34728  btwnconn1lem12  34729  segcon2  34736  seglecgr12im  34741  unbdqndv2  35020  lplnexllnN  38073  paddasslem9  38337  paddasslem15  38343  pmodlem2  38356  lhp2lt  38510  isthincd2  47144  mndtccatid  47199
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