Theorem simpr2l 1232

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 1189	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

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:  poxp2  8184  ttrcltr  9785  ttrclss  9789  dmttrcl  9790  ttrclselem2  9795  oppccatid  17779  subccatid  17910  setccatid  18151  catccatid  18173  estrccatid  18200  xpccatid  18257  kerf1ghm  19287  gsmsymgreqlem1  19472  nllyidm  23518  noinfbnd1lem5  27790  ax5seg  28971  3pthdlem1  30196  segconeq  35974  ifscgr  36008  brofs2  36041  brifs2  36042  idinside  36048  btwnconn1lem8  36058  btwnconn1lem12  36062  segcon2  36069  segletr  36078  outsidele  36096  unbdqndv2  36477  lplnexllnN  39521  paddasslem9  39785  pmodlem2  39804  lhp2lt  39958  cdlemc3  40150  cdlemc4  40151  cdlemd1  40155  cdleme3b  40186  cdleme3c  40187  cdleme42ke  40442  cdlemg4c  40569  clnbgrgrimlem  47785  isthincd2  48705  mndtccatid  48760