Theorem simp2lr 1241

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp2lr	⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Proof of Theorem simp2lr

Step	Hyp	Ref	Expression
1		simplr 768	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant2 1134	1 ⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 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:  fpr3g  8326  tfrlem5  8436  omeu  8641  expmordi  14217  4sqlem18  17009  vdwlem10  17037  mvrf1  22029  mdetuni0  22648  mdetmul  22650  tsmsxp  24184  ax5seglem3  28964  btwnconn1lem1  36051  btwnconn1lem3  36053  btwnconn1lem4  36054  btwnconn1lem5  36055  btwnconn1lem6  36056  btwnconn1lem7  36057  linethru  36117  lshpkrlem6  39071  athgt  39413  2llnjN  39524  dalaw  39843  cdlemb2  39998  4atexlemex6  40031  cdleme01N  40178  cdleme0ex2N  40181  cdleme7aa  40199  cdleme7e  40204  cdlemg33c0  40659  dihmeetlem3N  41262  pellex  42791