Theorem simpr1r 1233

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 773	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr1 1190	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  poxp2  8093  oppccatid  17685  subccatid  17813  setccatid  18051  catccatid  18073  estrccatid  18098  xpccatid  18154  gsmsymgreqlem1  19405  dmdprdsplit  20024  neitr  23145  neitx  23572  tx1stc  23615  utop3cls  24216  metustsym  24520  clwwlkccat  30060  3pthdlem1  30234  archiabllem1  33254  esumpcvgval  34222  esum2d  34237  ifscgr  36226  btwnconn1lem8  36276  btwnconn1lem11  36279  btwnconn1lem12  36280  segletr  36296  broutsideof3  36308  unbdqndv2  36771  lhp2lt  40447  cdlemf2  41008  cdlemn11pre  41656  stoweidlem60  46488  ssccatid  49547  isthincd2  49912  mndtccatid  50062