Theorem simpr1r 1244

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 782	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr1 1201	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  poxp2  8118  oppccatid  17734  subccatid  17862  setccatid  18100  catccatid  18122  estrccatid  18147  xpccatid  18203  gsmsymgreqlem1  19453  dmdprdsplit  20072  neitr  23220  neitx  23647  tx1stc  23690  utop3cls  24291  metustsym  24595  clwwlkccat  30138  3pthdlem1  30312  archiabllem1  33334  esumpcvgval  34336  esum2d  34351  ifscgr  36358  btwnconn1lem8  36408  btwnconn1lem11  36411  btwnconn1lem12  36412  segletr  36428  broutsideof3  36440  unbdqndv2  36913  lhp2lt  40589  cdlemf2  41150  cdlemn11pre  41798  stoweidlem60  46598  ssccatid  49657  isthincd2  50022  mndtccatid  50172