Theorem simp2lr 1260

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 781	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant2 1152	1 ⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  fpr3g  8291  tfrlem5  8375  omeu  8579  expmordi  14223  4sqlem18  17047  vdwlem10  17075  mvrf1  22172  mdetuni0  22815  mdetmul  22817  tsmsxp  24349  ax5seglem3  29318  btwnconn1lem1  36600  btwnconn1lem3  36602  btwnconn1lem4  36603  btwnconn1lem5  36604  btwnconn1lem6  36605  btwnconn1lem7  36606  linethru  36666  lshpkrlem6  39930  athgt  40271  2llnjN  40382  dalaw  40701  cdlemb2  40856  4atexlemex6  40889  cdleme01N  41036  cdleme0ex2N  41039  cdleme7aa  41057  cdleme7e  41062  cdlemg33c0  41517  dihmeetlem3N  42120  pellex  43603