Theorem simplr3 1043

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

Assertion

Ref	Expression
simplr3	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Proof of Theorem simplr3

Step	Hyp	Ref	Expression
1		simpr3 1007	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  netap  7337  prarloclemlt  7577  prarloclemlo  7578  resqrexlemdecn  11194  summodclem2  11564  isumss2  11575  pcdvdstr  12521  ennnfoneleminc  12653  prdssgrpd  13117  prdsmndd  13150  grprcan  13239  mulgnn0dir  13358  mulgdir  13360  mulgass  13365  lmodprop2d  13980  lssintclm  14016  psrbaglesuppg  14302  restopnb  14501  blsscls2  14813