Theorem simpr2r 1246

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 782	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr2 1202	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  poxp2  8118  poxp3  8125  frrlem8  8269  ttrcltr  9668  ttrclss  9672  rnttrcl  9674  ttrclselem2  9678  oppccatid  17734  subccatid  17862  setccatid  18100  catccatid  18122  estrccatid  18147  xpccatid  18203  kerf1ghm  19270  gsmsymgreqlem1  19453  ax5seg  29085  3pthdlem1  30312  segconeq  36324  ifscgr  36358  brofs2  36391  brifs2  36392  idinside  36398  btwnconn1lem8  36408  btwnconn1lem11  36411  btwnconn1lem12  36412  segcon2  36419  seglecgr12im  36424  unbdqndv2  36913  lplnexllnN  40152  paddasslem9  40416  paddasslem15  40422  pmodlem2  40435  lhp2lt  40589  ssccatid  49657  isthincd2  50022  mndtccatid  50172