Theorem simpr2r 1252

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

Assertion

Ref	Expression
simpr2r	⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜓)

Proof of Theorem simpr2r

Step	Hyp	Ref	Expression
1		simprr 784	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr2 1208	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜓)

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  poxp3  8147  frrlem8  8291  ttrcltr  9686  ttrclss  9690  rnttrcl  9692  ttrclselem2  9696  oppccatid  17776  subccatid  17904  setccatid  18142  catccatid  18164  estrccatid  18189  xpccatid  18245  kerf1ghm  19318  gsmsymgreqlem1  19501  ax5seg  29266  3pthdlem1  30493  segconeq  36480  ifscgr  36514  brofs2  36547  brifs2  36548  idinside  36554  btwnconn1lem8  36564  btwnconn1lem11  36567  btwnconn1lem12  36568  segcon2  36575  seglecgr12im  36580  unbdqndv2  37078  lplnexllnN  40316  paddasslem9  40580  paddasslem15  40586  pmodlem2  40599  lhp2lt  40753  ssccatid  49827  isthincd2  50192  mndtccatid  50342