Theorem simpr1l 1230

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

Assertion

Ref	Expression
simpr1l	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

Proof of Theorem simpr1l

Step	Hyp	Ref	Expression
1		simprl 770	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr1 1188	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

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  poxp3  8191  oppccatid  17779  subccatid  17910  setccatid  18151  catccatid  18173  estrccatid  18200  xpccatid  18257  gsmsymgreqlem1  19472  dmdprdsplit  20091  neiptopnei  23161  neitr  23209  neitx  23636  tx1stc  23679  utop3cls  24281  metustsym  24589  ax5seg  28971  clwwlkccat  30022  3pthdlem1  30196  esumpcvgval  34042  esum2d  34057  ifscgr  36008  brofs2  36041  brifs2  36042  btwnconn1lem8  36058  btwnconn1lem12  36062  seglecgr12im  36074  unbdqndv2  36477  lhp2lt  39958  cdlemd1  40155  cdleme3b  40186  cdleme3c  40187  cdleme3e  40189  cdlemf2  40519  cdlemg4c  40569  cdlemn11pre  41167  dihmeetlem12N  41275  stoweidlem60  45981  isthincd2  48705  mndtccatid  48760