Theorem simpr1r 1231

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)

Assertion

Ref	Expression
simpr1r	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Proof of Theorem simpr1r

Step	Hyp	Ref	Expression
1		simprr 772	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr1 1188	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  poxp2  8184  oppccatid  17779  subccatid  17910  setccatid  18151  catccatid  18173  estrccatid  18200  xpccatid  18257  gsmsymgreqlem1  19472  dmdprdsplit  20091  neitr  23209  neitx  23636  tx1stc  23679  utop3cls  24281  metustsym  24589  clwwlkccat  30022  3pthdlem1  30196  archiabllem1  33173  esumpcvgval  34042  esum2d  34057  ifscgr  36008  btwnconn1lem8  36058  btwnconn1lem11  36061  btwnconn1lem12  36062  segletr  36078  broutsideof3  36090  unbdqndv2  36477  lhp2lt  39958  cdlemf2  40519  cdlemn11pre  41167  stoweidlem60  45981  isthincd2  48705  mndtccatid  48760