Theorem simpr1l 1228

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 767	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr1 1186	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 394   ∧ w3a 1085

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 206  df-an 395  df-3an 1087

This theorem is referenced by:  poxp2  8131  poxp3  8138  oppccatid  17669  subccatid  17800  setccatid  18038  catccatid  18060  estrccatid  18087  xpccatid  18144  gsmsymgreqlem1  19339  dmdprdsplit  19958  neiptopnei  22856  neitr  22904  neitx  23331  tx1stc  23374  utop3cls  23976  metustsym  24284  ax5seg  28463  clwwlkccat  29510  3pthdlem1  29684  esumpcvgval  33374  esum2d  33389  ifscgr  35320  brofs2  35353  brifs2  35354  btwnconn1lem8  35370  btwnconn1lem12  35374  seglecgr12im  35386  unbdqndv2  35690  lhp2lt  39175  cdlemd1  39372  cdleme3b  39403  cdleme3c  39404  cdleme3e  39406  cdlemf2  39736  cdlemg4c  39786  cdlemn11pre  40384  dihmeetlem12N  40492  stoweidlem60  45074  isthincd2  47745  mndtccatid  47800