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  7292  omeu  8506  ntrivcvgmul  15811  tsmsxp  24071  tgqioo  24716  ovolunlem2  25427  plyadd  26150  plymul  26151  coeeu  26158  nosupbnd1lem2  27649  noinfbnd1lem2  27664  tghilberti2  28617  btwnconn1lem2  36153  btwnconn1lem3  36154  btwnconn1lem4  36155  athgt  39575  2llnjN  39686  4atlem12b  39730  lncmp  39902  cdlema2N  39911  cdleme21ct  40448  cdleme24  40471  cdleme27a  40486  cdleme28  40492  cdleme42b  40597  cdlemf  40682  dihlsscpre  41353  dihord4  41377  dihord5apre  41381  pellex  42952  jm2.27  43125