Theorem simpr1l 1247

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 782	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr1 1205	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  poxp2  8127  poxp3  8134  oppccatid  17765  subccatid  17893  setccatid  18131  catccatid  18153  estrccatid  18178  xpccatid  18234  gsmsymgreqlem1  19491  dmdprdsplit  20110  neiptopnei  23250  neitr  23298  neitx  23725  tx1stc  23768  utop3cls  24369  metustsym  24673  ax5seg  29197  clwwlkccat  30250  3pthdlem1  30424  esumpcvgval  34385  esum2d  34400  ifscgr  36407  brofs2  36440  brifs2  36441  btwnconn1lem8  36457  btwnconn1lem12  36461  seglecgr12im  36473  unbdqndv2  36962  lhp2lt  40637  cdlemd1  40834  cdleme3b  40865  cdleme3c  40866  cdleme3e  40868  cdlemf2  41198  cdlemg4c  41248  cdlemn11pre  41846  dihmeetlem12N  41954  stoweidlem60  46632  ssccatid  49701  isthincd2  50066  mndtccatid  50216