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  8079  oppccatid  17631  subccatid  17759  setccatid  17997  catccatid  18019  estrccatid  18044  xpccatid  18100  gsmsymgreqlem1  19348  dmdprdsplit  19967  neitr  23101  neitx  23528  tx1stc  23571  utop3cls  24172  metustsym  24476  clwwlkccat  29977  3pthdlem1  30151  archiabllem1  33169  esumpcvgval  34098  esum2d  34113  ifscgr  36095  btwnconn1lem8  36145  btwnconn1lem11  36148  btwnconn1lem12  36149  segletr  36165  broutsideof3  36177  unbdqndv2  36562  lhp2lt  40106  cdlemf2  40667  cdlemn11pre  41315  stoweidlem60  46163  ssccatid  49178  isthincd2  49543  mndtccatid  49693