Theorem simpr2r 1231

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 769	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr2 1187	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 394   ∧ w3a 1085

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 206  df-an 395  df-3an 1087

This theorem is referenced by:  poxp2  8131  poxp3  8138  frrlem8  8280  ttrcltr  9713  ttrclss  9717  rnttrcl  9719  ttrclselem2  9723  oppccatid  17669  subccatid  17800  setccatid  18038  catccatid  18060  estrccatid  18087  xpccatid  18144  kerf1ghm  19161  gsmsymgreqlem1  19339  ax5seg  28463  3pthdlem1  29684  segconeq  35286  ifscgr  35320  brofs2  35353  brifs2  35354  idinside  35360  btwnconn1lem8  35370  btwnconn1lem11  35373  btwnconn1lem12  35374  segcon2  35381  seglecgr12im  35386  unbdqndv2  35690  lplnexllnN  38738  paddasslem9  39002  paddasslem15  39008  pmodlem2  39021  lhp2lt  39175  isthincd2  47745  mndtccatid  47800