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  7330  omeu  8552  ntrivcvgmul  15875  tsmsxp  24049  tgqioo  24695  ovolunlem2  25406  plyadd  26129  plymul  26130  coeeu  26137  nosupbnd1lem2  27628  noinfbnd1lem2  27643  tghilberti2  28572  btwnconn1lem2  36083  btwnconn1lem3  36084  btwnconn1lem4  36085  athgt  39457  2llnjN  39568  4atlem12b  39612  lncmp  39784  cdlema2N  39793  cdleme21ct  40330  cdleme24  40353  cdleme27a  40368  cdleme28  40374  cdleme42b  40479  cdlemf  40564  dihlsscpre  41235  dihord4  41259  dihord5apre  41263  pellex  42830  jm2.27  43004