Theorem simp2lr 1260

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp2lr	⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Proof of Theorem simp2lr

Step	Hyp	Ref	Expression
1		simplr 781	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant2 1152	1 ⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  fpr3g  8288  tfrlem5  8372  omeu  8576  expmordi  14235  4sqlem18  17060  vdwlem10  17088  mvrf1  22206  mdetuni0  22849  mdetmul  22851  tsmsxp  24387  ax5seglem3  29396  btwnconn1lem1  36675  btwnconn1lem3  36677  btwnconn1lem4  36678  btwnconn1lem5  36679  btwnconn1lem6  36680  btwnconn1lem7  36681  linethru  36741  lshpkrlem6  39996  athgt  40337  2llnjN  40448  dalaw  40767  cdlemb2  40922  4atexlemex6  40955  cdleme01N  41102  cdleme0ex2N  41105  cdleme7aa  41123  cdleme7e  41128  cdlemg33c0  41583  dihmeetlem3N  42186  pellex  43684