MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp3ll Structured version   Visualization version   GIF version

Theorem simp3ll 1245
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 767 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜑)
213ad2ant3 1136 1 ((𝜃𝜏 ∧ ((𝜑𝜓) ∧ 𝜒)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  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 207  df-an 396  df-3an 1089
This theorem is referenced by:  f1oiso2  7372  omeu  8623  ntrivcvgmul  15938  tsmsxp  24163  tgqioo  24821  ovolunlem2  25533  plyadd  26256  plymul  26257  coeeu  26264  nosupbnd1lem2  27754  noinfbnd1lem2  27769  tghilberti2  28646  btwnconn1lem2  36089  btwnconn1lem3  36090  btwnconn1lem12  36099  athgt  39458  2llnjN  39569  4atlem12b  39613  lncmp  39785  cdlema2N  39794  cdlemc2  40194  cdleme5  40242  cdleme11a  40262  cdleme21ct  40331  cdleme21  40339  cdleme22eALTN  40347  cdleme24  40354  cdleme27cl  40368  cdleme27a  40369  cdleme28  40375  cdleme36a  40462  cdleme42b  40480  cdleme48fvg  40502  cdlemf  40565  cdlemk39  40918  cdlemkid1  40924  dihlsscpre  41236  dihord4  41260  dihord5apre  41264  dihmeetlem20N  41328  mapdh9a  41791  pellex  42846  jm2.27  43020
  Copyright terms: Public domain W3C validator