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  8142  oppccatid  17731  subccatid  17859  setccatid  18097  catccatid  18119  estrccatid  18144  xpccatid  18200  gsmsymgreqlem1  19411  dmdprdsplit  20030  neitr  23118  neitx  23545  tx1stc  23588  utop3cls  24190  metustsym  24494  clwwlkccat  29971  3pthdlem1  30145  archiabllem1  33191  esumpcvgval  34109  esum2d  34124  ifscgr  36062  btwnconn1lem8  36112  btwnconn1lem11  36115  btwnconn1lem12  36116  segletr  36132  broutsideof3  36144  unbdqndv2  36529  lhp2lt  40020  cdlemf2  40581  cdlemn11pre  41229  stoweidlem60  46089  ssccatid  49039  isthincd2  49323  mndtccatid  49464