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  8267  tfrlem5  8351  omeu  8552  expmordi  14139  4sqlem18  16940  vdwlem10  16968  mvrf1  21902  mdetuni0  22515  mdetmul  22517  tsmsxp  24049  ax5seglem3  28865  btwnconn1lem1  36082  btwnconn1lem3  36084  btwnconn1lem4  36085  btwnconn1lem5  36086  btwnconn1lem6  36087  btwnconn1lem7  36088  linethru  36148  lshpkrlem6  39115  athgt  39457  2llnjN  39568  dalaw  39887  cdlemb2  40042  4atexlemex6  40075  cdleme01N  40222  cdleme0ex2N  40225  cdleme7aa  40243  cdleme7e  40248  cdlemg33c0  40703  dihmeetlem3N  41306  pellex  42830