Theorem simpr1l 1231

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 1189	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

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  8083  poxp3  8090  oppccatid  17643  subccatid  17771  setccatid  18009  catccatid  18031  estrccatid  18056  xpccatid  18112  gsmsymgreqlem1  19327  dmdprdsplit  19946  neiptopnei  23035  neitr  23083  neitx  23510  tx1stc  23553  utop3cls  24155  metustsym  24459  ax5seg  28901  clwwlkccat  29952  3pthdlem1  30126  esumpcvgval  34044  esum2d  34059  ifscgr  36017  brofs2  36050  brifs2  36051  btwnconn1lem8  36067  btwnconn1lem12  36071  seglecgr12im  36083  unbdqndv2  36484  lhp2lt  39980  cdlemd1  40177  cdleme3b  40208  cdleme3c  40209  cdleme3e  40211  cdlemf2  40541  cdlemg4c  40591  cdlemn11pre  41189  dihmeetlem12N  41297  stoweidlem60  46042  ssccatid  49058  isthincd2  49423  mndtccatid  49573