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 780	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1153	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

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 210  df-an 401  df-3an 1105

This theorem is referenced by:  f1oiso2  7352  omeu  8571  ntrivcvgmul  15958  tsmsxp  24293  tgqioo  24938  ovolunlem2  25638  plyadd  26355  plymul  26356  coeeu  26363  nosupbnd1lem2  27851  noinfbnd1lem2  27866  tghilberti2  28889  btwnconn1lem2  36558  btwnconn1lem3  36559  btwnconn1lem4  36560  athgt  40208  2llnjN  40319  4atlem12b  40363  lncmp  40535  cdlema2N  40544  cdleme21ct  41081  cdleme24  41104  cdleme27a  41119  cdleme28  41125  cdleme42b  41230  cdlemf  41315  dihlsscpre  41986  dihord4  42010  dihord5apre  42014  pellex  43542  jm2.27  43715