Theorem simpr1l 1243

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 780	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr1 1201	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

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  oppccatid  17734  subccatid  17862  setccatid  18100  catccatid  18122  estrccatid  18147  xpccatid  18203  gsmsymgreqlem1  19453  dmdprdsplit  20072  neiptopnei  23172  neitr  23220  neitx  23647  tx1stc  23690  utop3cls  24291  metustsym  24595  ax5seg  29085  clwwlkccat  30138  3pthdlem1  30312  esumpcvgval  34336  esum2d  34351  ifscgr  36358  brofs2  36391  brifs2  36392  btwnconn1lem8  36408  btwnconn1lem12  36412  seglecgr12im  36424  unbdqndv2  36913  lhp2lt  40589  cdlemd1  40786  cdleme3b  40817  cdleme3c  40818  cdleme3e  40820  cdlemf2  41150  cdlemg4c  41200  cdlemn11pre  41798  dihmeetlem12N  41906  stoweidlem60  46598  ssccatid  49657  isthincd2  50022  mndtccatid  50172