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  8227  tfrlem5  8311  omeu  8512  expmordi  14090  4sqlem18  16890  vdwlem10  16918  mvrf1  21941  mdetuni0  22565  mdetmul  22567  tsmsxp  24099  ax5seglem3  29004  btwnconn1lem1  36281  btwnconn1lem3  36283  btwnconn1lem4  36284  btwnconn1lem5  36285  btwnconn1lem6  36286  btwnconn1lem7  36287  linethru  36347  lshpkrlem6  39371  athgt  39712  2llnjN  39823  dalaw  40142  cdlemb2  40297  4atexlemex6  40330  cdleme01N  40477  cdleme0ex2N  40480  cdleme7aa  40498  cdleme7e  40503  cdlemg33c0  40958  dihmeetlem3N  41561  pellex  43073