Theorem simpr1l 1231

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 770	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr1 1189	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 1088

This theorem is referenced by:  poxp2  8122  poxp3  8129  oppccatid  17680  subccatid  17808  setccatid  18046  catccatid  18068  estrccatid  18093  xpccatid  18149  gsmsymgreqlem1  19360  dmdprdsplit  19979  neiptopnei  23019  neitr  23067  neitx  23494  tx1stc  23537  utop3cls  24139  metustsym  24443  ax5seg  28865  clwwlkccat  29919  3pthdlem1  30093  esumpcvgval  34068  esum2d  34083  ifscgr  36032  brofs2  36065  brifs2  36066  btwnconn1lem8  36082  btwnconn1lem12  36086  seglecgr12im  36098  unbdqndv2  36499  lhp2lt  39995  cdlemd1  40192  cdleme3b  40223  cdleme3c  40224  cdleme3e  40226  cdlemf2  40556  cdlemg4c  40606  cdlemn11pre  41204  dihmeetlem12N  41312  stoweidlem60  46058  ssccatid  49061  isthincd2  49426  mndtccatid  49576