Theorem simpr2l 1231

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

Assertion

Ref	Expression
simpr2l	⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Proof of Theorem simpr2l

Step	Hyp	Ref	Expression
1		simprl 768	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr2 1188	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 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:  ttrcltr  9474  ttrclss  9478  dmttrcl  9479  ttrclselem2  9484  oppccatid  17430  subccatid  17561  setccatid  17799  catccatid  17821  estrccatid  17848  xpccatid  17905  gsmsymgreqlem1  19038  kerf1ghm  19987  nllyidm  22640  ax5seg  27306  3pthdlem1  28528  poxp2  33790  noinfbnd1lem5  33930  segconeq  34312  ifscgr  34346  brofs2  34379  brifs2  34380  idinside  34386  btwnconn1lem8  34396  btwnconn1lem12  34400  segcon2  34407  segletr  34416  outsidele  34434  unbdqndv2  34691  lplnexllnN  37578  paddasslem9  37842  pmodlem2  37861  lhp2lt  38015  cdlemc3  38207  cdlemc4  38208  cdlemd1  38212  cdleme3b  38243  cdleme3c  38244  cdleme42ke  38499  cdlemg4c  38626  isthincd2  46319  mndtccatid  46374