Theorem simpr2l 1251

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 782	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr2 1208	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

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 210  df-an 401  df-3an 1105

This theorem is referenced by:  poxp2  8140  ttrcltr  9686  ttrclss  9690  dmttrcl  9691  ttrclselem2  9696  oppccatid  17776  subccatid  17904  setccatid  18142  catccatid  18164  estrccatid  18189  xpccatid  18245  kerf1ghm  19318  gsmsymgreqlem1  19501  nllyidm  23627  noinfbnd1lem5  27869  ax5seg  29266  3pthdlem1  30493  segconeq  36480  ifscgr  36514  brofs2  36547  brifs2  36548  idinside  36554  btwnconn1lem8  36564  btwnconn1lem12  36568  segcon2  36575  segletr  36584  outsidele  36602  unbdqndv2  37078  lplnexllnN  40316  paddasslem9  40580  pmodlem2  40599  lhp2lt  40753  cdlemc3  40945  cdlemc4  40946  cdlemd1  40950  cdleme3b  40981  cdleme3c  40982  cdleme42ke  41237  cdlemg4c  41364  clnbgrgrimlem  48675  ssccatid  49827  isthincd2  50192  mndtccatid  50342