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 770	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr1 1187	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 396   ∧ 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 206  df-an 397  df-3an 1088

This theorem is referenced by:  oppccatid  17430  subccatid  17561  setccatid  17799  catccatid  17821  estrccatid  17848  xpccatid  17905  gsmsymgreqlem1  19038  dmdprdsplit  19650  neitr  22331  neitx  22758  tx1stc  22801  utop3cls  23403  metustsym  23711  clwwlkccat  28354  3pthdlem1  28528  archiabllem1  31447  esumpcvgval  32046  esum2d  32061  poxp2  33790  ifscgr  34346  btwnconn1lem8  34396  btwnconn1lem11  34399  btwnconn1lem12  34400  segletr  34416  broutsideof3  34428  unbdqndv2  34691  lhp2lt  38015  cdlemf2  38576  cdlemn11pre  39224  stoweidlem60  43601  isthincd2  46319  mndtccatid  46374