Theorem simpr2r 1234

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 772	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr2 1190	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  8122  poxp3  8129  frrlem8  8272  ttrcltr  9669  ttrclss  9673  rnttrcl  9675  ttrclselem2  9679  oppccatid  17680  subccatid  17808  setccatid  18046  catccatid  18068  estrccatid  18093  xpccatid  18149  kerf1ghm  19179  gsmsymgreqlem1  19360  ax5seg  28865  3pthdlem1  30093  segconeq  35998  ifscgr  36032  brofs2  36065  brifs2  36066  idinside  36072  btwnconn1lem8  36082  btwnconn1lem11  36085  btwnconn1lem12  36086  segcon2  36093  seglecgr12im  36098  unbdqndv2  36499  lplnexllnN  39558  paddasslem9  39822  paddasslem15  39828  pmodlem2  39841  lhp2lt  39995  ssccatid  49061  isthincd2  49426  mndtccatid  49576