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  8122  oppccatid  17680  subccatid  17808  setccatid  18046  catccatid  18068  estrccatid  18093  xpccatid  18149  gsmsymgreqlem1  19360  dmdprdsplit  19979  neitr  23067  neitx  23494  tx1stc  23537  utop3cls  24139  metustsym  24443  clwwlkccat  29919  3pthdlem1  30093  archiabllem1  33147  esumpcvgval  34068  esum2d  34083  ifscgr  36032  btwnconn1lem8  36082  btwnconn1lem11  36085  btwnconn1lem12  36086  segletr  36102  broutsideof3  36114  unbdqndv2  36499  lhp2lt  39995  cdlemf2  40556  cdlemn11pre  41204  stoweidlem60  46058  ssccatid  49061  isthincd2  49426  mndtccatid  49576