Theorem simpr1r 1232

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 772	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr1 1189	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

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  8083  oppccatid  17643  subccatid  17771  setccatid  18009  catccatid  18031  estrccatid  18056  xpccatid  18112  gsmsymgreqlem1  19327  dmdprdsplit  19946  neitr  23083  neitx  23510  tx1stc  23553  utop3cls  24155  metustsym  24459  clwwlkccat  29952  3pthdlem1  30126  archiabllem1  33145  esumpcvgval  34044  esum2d  34059  ifscgr  36017  btwnconn1lem8  36067  btwnconn1lem11  36070  btwnconn1lem12  36071  segletr  36087  broutsideof3  36099  unbdqndv2  36484  lhp2lt  39980  cdlemf2  40541  cdlemn11pre  41189  stoweidlem60  46042  ssccatid  49058  isthincd2  49423  mndtccatid  49573