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  8142  poxp3  8149  oppccatid  17731  subccatid  17859  setccatid  18097  catccatid  18119  estrccatid  18144  xpccatid  18200  gsmsymgreqlem1  19411  dmdprdsplit  20030  neiptopnei  23070  neitr  23118  neitx  23545  tx1stc  23588  utop3cls  24190  metustsym  24494  ax5seg  28917  clwwlkccat  29971  3pthdlem1  30145  esumpcvgval  34109  esum2d  34124  ifscgr  36062  brofs2  36095  brifs2  36096  btwnconn1lem8  36112  btwnconn1lem12  36116  seglecgr12im  36128  unbdqndv2  36529  lhp2lt  40020  cdlemd1  40217  cdleme3b  40248  cdleme3c  40249  cdleme3e  40251  cdlemf2  40581  cdlemg4c  40631  cdlemn11pre  41229  dihmeetlem12N  41337  stoweidlem60  46089  ssccatid  49039  isthincd2  49323  mndtccatid  49464