Theorem simpr2l 1233

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)

Assertion

Ref	Expression
simpr2l	⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Proof of Theorem simpr2l

Step	Hyp	Ref	Expression
1		simprl 770	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr2 1190	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 1088

This theorem is referenced by:  poxp2  8076  ttrcltr  9612  ttrclss  9616  dmttrcl  9617  ttrclselem2  9622  oppccatid  17625  subccatid  17753  setccatid  17991  catccatid  18013  estrccatid  18038  xpccatid  18094  kerf1ghm  19126  gsmsymgreqlem1  19309  nllyidm  23374  noinfbnd1lem5  27637  ax5seg  28883  3pthdlem1  30108  segconeq  35994  ifscgr  36028  brofs2  36061  brifs2  36062  idinside  36068  btwnconn1lem8  36078  btwnconn1lem12  36082  segcon2  36089  segletr  36098  outsidele  36116  unbdqndv2  36495  lplnexllnN  39553  paddasslem9  39817  pmodlem2  39836  lhp2lt  39990  cdlemc3  40182  cdlemc4  40183  cdlemd1  40187  cdleme3b  40218  cdleme3c  40219  cdleme42ke  40474  cdlemg4c  40601  clnbgrgrimlem  47927  ssccatid  49067  isthincd2  49432  mndtccatid  49582