Theorem simpr1r 1229

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)

Assertion

Ref	Expression
simpr1r	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Proof of Theorem simpr1r

Step	Hyp	Ref	Expression
1		simprr 769	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr1 1186	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 394   ∧ 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 395  df-3an 1087

This theorem is referenced by:  poxp2  8131  oppccatid  17669  subccatid  17800  setccatid  18038  catccatid  18060  estrccatid  18087  xpccatid  18144  gsmsymgreqlem1  19339  dmdprdsplit  19958  neitr  22904  neitx  23331  tx1stc  23374  utop3cls  23976  metustsym  24284  clwwlkccat  29510  3pthdlem1  29684  archiabllem1  32609  esumpcvgval  33374  esum2d  33389  ifscgr  35320  btwnconn1lem8  35370  btwnconn1lem11  35373  btwnconn1lem12  35374  segletr  35390  broutsideof3  35402  unbdqndv2  35690  lhp2lt  39175  cdlemf2  39736  cdlemn11pre  40384  stoweidlem60  45074  isthincd2  47745  mndtccatid  47800