Theorem simp3lr 1247

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 769	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1136	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  f1oiso2  7300  omeu  8513  ntrivcvgmul  15858  tsmsxp  24130  tgqioo  24775  ovolunlem2  25475  plyadd  26192  plymul  26193  coeeu  26200  nosupbnd1lem2  27687  noinfbnd1lem2  27702  tghilberti2  28720  btwnconn1lem2  36286  btwnconn1lem3  36287  btwnconn1lem4  36288  athgt  39916  2llnjN  40027  4atlem12b  40071  lncmp  40243  cdlema2N  40252  cdleme21ct  40789  cdleme24  40812  cdleme27a  40827  cdleme28  40833  cdleme42b  40938  cdlemf  41023  dihlsscpre  41694  dihord4  41718  dihord5apre  41722  pellex  43281  jm2.27  43454