Theorem simplr3 1067

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 1031	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1004

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 1006

This theorem is referenced by:  netap  7478  prarloclemlt  7718  prarloclemlo  7719  ccatswrd  11260  pfxccat3  11324  resqrexlemdecn  11595  summodclem2  11966  isumss2  11977  pcdvdstr  12923  ennnfoneleminc  13055  prdssgrpd  13521  prdsmndd  13554  grprcan  13643  mulgnn0dir  13762  mulgdir  13764  mulgass  13769  lmodprop2d  14386  lssintclm  14422  psrbaglesuppg  14710  restopnb  14934  blsscls2  15246