Theorem simpr2l 1231

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 771	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr2 1188	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  8167  ttrcltr  9754  ttrclss  9758  dmttrcl  9759  ttrclselem2  9764  oppccatid  17766  subccatid  17897  setccatid  18138  catccatid  18160  estrccatid  18187  xpccatid  18244  kerf1ghm  19278  gsmsymgreqlem1  19463  nllyidm  23513  noinfbnd1lem5  27787  ax5seg  28968  3pthdlem1  30193  segconeq  35992  ifscgr  36026  brofs2  36059  brifs2  36060  idinside  36066  btwnconn1lem8  36076  btwnconn1lem12  36080  segcon2  36087  segletr  36096  outsidele  36114  unbdqndv2  36494  lplnexllnN  39547  paddasslem9  39811  pmodlem2  39830  lhp2lt  39984  cdlemc3  40176  cdlemc4  40177  cdlemd1  40181  cdleme3b  40212  cdleme3c  40213  cdleme42ke  40468  cdlemg4c  40595  clnbgrgrimlem  47839  isthincd2  48838  mndtccatid  48896