Theorem simp3lr 1264

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

Assertion

Ref	Expression
simp3lr	⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Proof of Theorem simp3lr

Step	Hyp	Ref	Expression
1		simplr 781	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1153	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 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:  f1oiso2  7357  omeu  8576  ntrivcvgmul  15995  tsmsxp  24387  tgqioo  25032  ovolunlem2  25732  plyadd  26450  plymul  26451  coeeu  26458  nosupbnd1lem2  27953  noinfbnd1lem2  27968  tghilberti2  28993  btwnconn1lem2  36676  btwnconn1lem3  36677  btwnconn1lem4  36678  athgt  40337  2llnjN  40448  4atlem12b  40492  lncmp  40664  cdlema2N  40673  cdleme21ct  41210  cdleme24  41233  cdleme27a  41248  cdleme28  41254  cdleme42b  41359  cdlemf  41444  dihlsscpre  42115  dihord4  42139  dihord5apre  42143  pellex  43684  jm2.27  43857