Theorem simpr1r 1250

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 784	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr1 1207	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

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 210  df-an 401  df-3an 1105

This theorem is referenced by:  poxp2  8140  oppccatid  17776  subccatid  17904  setccatid  18142  catccatid  18164  estrccatid  18189  xpccatid  18245  gsmsymgreqlem1  19501  dmdprdsplit  20120  neitr  23318  neitx  23745  tx1stc  23788  utop3cls  24389  metustsym  24693  clwwlkccat  30319  3pthdlem1  30493  archiabllem1  33491  esumpcvgval  34446  esum2d  34461  ifscgr  36514  btwnconn1lem8  36564  btwnconn1lem11  36567  btwnconn1lem12  36568  segletr  36584  broutsideof3  36596  unbdqndv2  37078  lhp2lt  40753  cdlemf2  41314  cdlemn11pre  41962  stoweidlem60  46754  ssccatid  49827  isthincd2  50192  mndtccatid  50342