Theorem simpr2l 1245

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 780	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr2 1202	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  poxp2  8118  ttrcltr  9668  ttrclss  9672  dmttrcl  9673  ttrclselem2  9678  oppccatid  17734  subccatid  17862  setccatid  18100  catccatid  18122  estrccatid  18147  xpccatid  18203  kerf1ghm  19270  gsmsymgreqlem1  19453  nllyidm  23529  noinfbnd1lem5  27768  ax5seg  29085  3pthdlem1  30312  segconeq  36324  ifscgr  36358  brofs2  36391  brifs2  36392  idinside  36398  btwnconn1lem8  36408  btwnconn1lem12  36412  segcon2  36419  segletr  36428  outsidele  36446  unbdqndv2  36913  lplnexllnN  40152  paddasslem9  40416  pmodlem2  40435  lhp2lt  40589  cdlemc3  40781  cdlemc4  40782  cdlemd1  40786  cdleme3b  40817  cdleme3c  40818  cdleme42ke  41073  cdlemg4c  41200  clnbgrgrimlem  48519  ssccatid  49657  isthincd2  50022  mndtccatid  50172