Theorem simpr1l 1229

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)

Assertion

Ref	Expression
simpr1l	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

Proof of Theorem simpr1l

Step	Hyp	Ref	Expression
1		simprl 768	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr1 1187	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

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  neiptopnei  22283  neitr  22331  neitx  22758  tx1stc  22801  utop3cls  23403  metustsym  23711  ax5seg  27306  clwwlkccat  28354  3pthdlem1  28528  esumpcvgval  32046  esum2d  32061  poxp2  33790  ifscgr  34346  brofs2  34379  brifs2  34380  btwnconn1lem8  34396  btwnconn1lem12  34400  seglecgr12im  34412  unbdqndv2  34691  lhp2lt  38015  cdlemd1  38212  cdleme3b  38243  cdleme3c  38244  cdleme3e  38246  cdlemf2  38576  cdlemg4c  38626  cdlemn11pre  39224  dihmeetlem12N  39332  stoweidlem60  43601  isthincd2  46319  mndtccatid  46374