Theorem simpr1l 1232

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 771	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr1 1190	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  8093  poxp3  8100  oppccatid  17685  subccatid  17813  setccatid  18051  catccatid  18073  estrccatid  18098  xpccatid  18154  gsmsymgreqlem1  19405  dmdprdsplit  20024  neiptopnei  23097  neitr  23145  neitx  23572  tx1stc  23615  utop3cls  24216  metustsym  24520  ax5seg  29007  clwwlkccat  30060  3pthdlem1  30234  esumpcvgval  34222  esum2d  34237  ifscgr  36226  brofs2  36259  brifs2  36260  btwnconn1lem8  36276  btwnconn1lem12  36280  seglecgr12im  36292  unbdqndv2  36771  lhp2lt  40447  cdlemd1  40644  cdleme3b  40675  cdleme3c  40676  cdleme3e  40678  cdlemf2  41008  cdlemg4c  41058  cdlemn11pre  41656  dihmeetlem12N  41764  stoweidlem60  46488  ssccatid  49547  isthincd2  49912  mndtccatid  50062