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 395   ∧ 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 396  df-3an 1087

This theorem is referenced by:  frrlem8  8080  oppccatid  17347  subccatid  17477  setccatid  17715  catccatid  17737  estrccatid  17764  xpccatid  17821  gsmsymgreqlem1  18953  kerf1ghm  19902  ax5seg  27209  3pthdlem1  28429  ttrcltr  33702  ttrclss  33706  rnttrcl  33708  ttrclselem2  33712  poxp2  33717  segconeq  34239  ifscgr  34273  brofs2  34306  brifs2  34307  idinside  34313  btwnconn1lem8  34323  btwnconn1lem11  34326  btwnconn1lem12  34327  segcon2  34334  seglecgr12im  34339  unbdqndv2  34618  lplnexllnN  37505  paddasslem9  37769  paddasslem15  37775  pmodlem2  37788  lhp2lt  37942  isthincd2  46207  mndtccatid  46260