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 395   ∧ 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 396  df-3an 1087

This theorem is referenced by:  oppccatid  17347  subccatid  17477  setccatid  17715  catccatid  17737  estrccatid  17764  xpccatid  17821  gsmsymgreqlem1  18953  dmdprdsplit  19565  neiptopnei  22191  neitr  22239  neitx  22666  tx1stc  22709  utop3cls  23311  metustsym  23617  ax5seg  27209  clwwlkccat  28255  3pthdlem1  28429  esumpcvgval  31946  esum2d  31961  poxp2  33717  ifscgr  34273  brofs2  34306  brifs2  34307  btwnconn1lem8  34323  btwnconn1lem12  34327  seglecgr12im  34339  unbdqndv2  34618  lhp2lt  37942  cdlemd1  38139  cdleme3b  38170  cdleme3c  38171  cdleme3e  38173  cdlemf2  38503  cdlemg4c  38553  cdlemn11pre  39151  dihmeetlem12N  39259  stoweidlem60  43491  isthincd2  46207  mndtccatid  46260