Theorem simpr2r 1232

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 773	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr2 1188	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜓)

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  poxp3  8174  frrlem8  8317  ttrcltr  9754  ttrclss  9758  rnttrcl  9760  ttrclselem2  9764  oppccatid  17766  subccatid  17897  setccatid  18138  catccatid  18160  estrccatid  18187  xpccatid  18244  kerf1ghm  19278  gsmsymgreqlem1  19463  ax5seg  28968  3pthdlem1  30193  segconeq  35992  ifscgr  36026  brofs2  36059  brifs2  36060  idinside  36066  btwnconn1lem8  36076  btwnconn1lem11  36079  btwnconn1lem12  36080  segcon2  36087  seglecgr12im  36092  unbdqndv2  36494  lplnexllnN  39547  paddasslem9  39811  paddasslem15  39817  pmodlem2  39830  lhp2lt  39984  isthincd2  48838  mndtccatid  48896