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  7308  omeu  8522  ntrivcvgmul  15837  tsmsxp  24111  tgqioo  24756  ovolunlem2  25467  plyadd  26190  plymul  26191  coeeu  26198  nosupbnd1lem2  27689  noinfbnd1lem2  27704  tghilberti2  28722  btwnconn1lem2  36301  btwnconn1lem3  36302  btwnconn1lem4  36303  athgt  39826  2llnjN  39937  4atlem12b  39981  lncmp  40153  cdlema2N  40162  cdleme21ct  40699  cdleme24  40722  cdleme27a  40737  cdleme28  40743  cdleme42b  40848  cdlemf  40933  dihlsscpre  41604  dihord4  41628  dihord5apre  41632  pellex  43186  jm2.27  43359