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 397   ∧ w3a 1088

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 206  df-an 398  df-3an 1090

This theorem is referenced by:  poxp2  8129  oppccatid  17665  subccatid  17796  setccatid  18034  catccatid  18056  estrccatid  18083  xpccatid  18140  gsmsymgreqlem1  19298  dmdprdsplit  19917  neitr  22684  neitx  23111  tx1stc  23154  utop3cls  23756  metustsym  24064  clwwlkccat  29243  3pthdlem1  29417  archiabllem1  32339  esumpcvgval  33076  esum2d  33091  ifscgr  35016  btwnconn1lem8  35066  btwnconn1lem11  35069  btwnconn1lem12  35070  segletr  35086  broutsideof3  35098  unbdqndv2  35387  lhp2lt  38872  cdlemf2  39433  cdlemn11pre  40081  stoweidlem60  44776  isthincd2  47658  mndtccatid  47713