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Theorem simp1ll 1237
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp1ll ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃𝜏) → 𝜑)

Proof of Theorem simp1ll
StepHypRef Expression
1 simpll 766 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜑)
213ad2ant1 1134 1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃𝜏) → 𝜑)
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:  lspsolvlem  20619  1marepvsma1  21948  mdetunilem8  21984  madutpos  22007  ax5seg  27929  rabfodom  31475  measinblem  32876  btwnconn1lem2  34719  btwnconn1lem13  34730  athgt  37965  llnle  38027  lplnle  38049  lhpexle1  38517  lhpj1  38531  lhpat3  38555  ltrncnv  38655  cdleme16aN  38768  tendoicl  39305  cdlemk55b  39469  dihatexv  39847  dihglblem6  39849  limccog  43947  icccncfext  44214  stoweidlem31  44358  stoweidlem34  44361  stoweidlem49  44376  stoweidlem57  44384
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