Theorem simp3lr 1246

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 768	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1135	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

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:  f1oiso2  7345  omeu  8597  ntrivcvgmul  15918  tsmsxp  24093  tgqioo  24739  ovolunlem2  25451  plyadd  26174  plymul  26175  coeeu  26182  nosupbnd1lem2  27673  noinfbnd1lem2  27688  tghilberti2  28617  btwnconn1lem2  36106  btwnconn1lem3  36107  btwnconn1lem4  36108  athgt  39475  2llnjN  39586  4atlem12b  39630  lncmp  39802  cdlema2N  39811  cdleme21ct  40348  cdleme24  40371  cdleme27a  40386  cdleme28  40392  cdleme42b  40497  cdlemf  40582  dihlsscpre  41253  dihord4  41277  dihord5apre  41281  pellex  42858  jm2.27  43032