Theorem simpr1r 1230

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 1187	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  8167  oppccatid  17766  subccatid  17897  setccatid  18138  catccatid  18160  estrccatid  18187  xpccatid  18244  gsmsymgreqlem1  19463  dmdprdsplit  20082  neitr  23204  neitx  23631  tx1stc  23674  utop3cls  24276  metustsym  24584  clwwlkccat  30019  3pthdlem1  30193  archiabllem1  33183  esumpcvgval  34059  esum2d  34074  ifscgr  36026  btwnconn1lem8  36076  btwnconn1lem11  36079  btwnconn1lem12  36080  segletr  36096  broutsideof3  36108  unbdqndv2  36494  lhp2lt  39984  cdlemf2  40545  cdlemn11pre  41193  stoweidlem60  46016  isthincd2  48838  mndtccatid  48896