Theorem simpr1l 1229

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 771	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr1 1187	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  8167  poxp3  8174  oppccatid  17766  subccatid  17897  setccatid  18138  catccatid  18160  estrccatid  18187  xpccatid  18244  gsmsymgreqlem1  19463  dmdprdsplit  20082  neiptopnei  23156  neitr  23204  neitx  23631  tx1stc  23674  utop3cls  24276  metustsym  24584  ax5seg  28968  clwwlkccat  30019  3pthdlem1  30193  esumpcvgval  34059  esum2d  34074  ifscgr  36026  brofs2  36059  brifs2  36060  btwnconn1lem8  36076  btwnconn1lem12  36080  seglecgr12im  36092  unbdqndv2  36494  lhp2lt  39984  cdlemd1  40181  cdleme3b  40212  cdleme3c  40213  cdleme3e  40215  cdlemf2  40545  cdlemg4c  40595  cdlemn11pre  41193  dihmeetlem12N  41301  stoweidlem60  46016  isthincd2  48838  mndtccatid  48896