Theorem simpr2l 1233

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 770	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2antr2 1190	1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ 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 207  df-an 396  df-3an 1088

This theorem is referenced by:  poxp2  8122  ttrcltr  9669  ttrclss  9673  dmttrcl  9674  ttrclselem2  9679  oppccatid  17680  subccatid  17808  setccatid  18046  catccatid  18068  estrccatid  18093  xpccatid  18149  kerf1ghm  19179  gsmsymgreqlem1  19360  nllyidm  23376  noinfbnd1lem5  27639  ax5seg  28865  3pthdlem1  30093  segconeq  35998  ifscgr  36032  brofs2  36065  brifs2  36066  idinside  36072  btwnconn1lem8  36082  btwnconn1lem12  36086  segcon2  36093  segletr  36102  outsidele  36120  unbdqndv2  36499  lplnexllnN  39558  paddasslem9  39822  pmodlem2  39841  lhp2lt  39995  cdlemc3  40187  cdlemc4  40188  cdlemd1  40192  cdleme3b  40223  cdleme3c  40224  cdleme42ke  40479  cdlemg4c  40606  clnbgrgrimlem  47933  ssccatid  49061  isthincd2  49426  mndtccatid  49576