Theorem simpr2l 1230

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 767	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr2 1187	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 396  df-3an 1087

This theorem is referenced by:  oppccatid  17347  subccatid  17477  setccatid  17715  catccatid  17737  estrccatid  17764  xpccatid  17821  gsmsymgreqlem1  18953  kerf1ghm  19902  nllyidm  22548  ax5seg  27209  3pthdlem1  28429  ttrcltr  33702  ttrclss  33706  dmttrcl  33707  ttrclselem2  33712  poxp2  33717  noinfbnd1lem5  33857  segconeq  34239  ifscgr  34273  brofs2  34306  brifs2  34307  idinside  34313  btwnconn1lem8  34323  btwnconn1lem12  34327  segcon2  34334  segletr  34343  outsidele  34361  unbdqndv2  34618  lplnexllnN  37505  paddasslem9  37769  pmodlem2  37788  lhp2lt  37942  cdlemc3  38134  cdlemc4  38135  cdlemd1  38139  cdleme3b  38170  cdleme3c  38171  cdleme42ke  38426  cdlemg4c  38553  isthincd2  46207  mndtccatid  46260