Theorem simpr1l 1249

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 1207	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

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 1105

This theorem is referenced by:  poxp2  8140  poxp3  8147  oppccatid  17776  subccatid  17904  setccatid  18142  catccatid  18164  estrccatid  18189  xpccatid  18245  gsmsymgreqlem1  19501  dmdprdsplit  20120  neiptopnei  23270  neitr  23318  neitx  23745  tx1stc  23788  utop3cls  24389  metustsym  24693  ax5seg  29266  clwwlkccat  30319  3pthdlem1  30493  esumpcvgval  34446  esum2d  34461  ifscgr  36514  brofs2  36547  brifs2  36548  btwnconn1lem8  36564  btwnconn1lem12  36568  seglecgr12im  36580  unbdqndv2  37078  lhp2lt  40753  cdlemd1  40950  cdleme3b  40981  cdleme3c  40982  cdleme3e  40984  cdlemf2  41314  cdlemg4c  41364  cdlemn11pre  41962  dihmeetlem12N  42070  stoweidlem60  46754  ssccatid  49827  isthincd2  50192  mndtccatid  50342