Theorem simp2lr 1242

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 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:  fpr3g  8225  tfrlem5  8309  omeu  8510  expmordi  14092  4sqlem18  16892  vdwlem10  16920  mvrf1  21911  mdetuni0  22524  mdetmul  22526  tsmsxp  24058  ax5seglem3  28894  btwnconn1lem1  36060  btwnconn1lem3  36062  btwnconn1lem4  36063  btwnconn1lem5  36064  btwnconn1lem6  36065  btwnconn1lem7  36066  linethru  36126  lshpkrlem6  39093  athgt  39435  2llnjN  39546  dalaw  39865  cdlemb2  40020  4atexlemex6  40053  cdleme01N  40200  cdleme0ex2N  40203  cdleme7aa  40221  cdleme7e  40226  cdlemg33c0  40681  dihmeetlem3N  41284  pellex  42808