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  7339  prarloclemlt  7579  prarloclemlo  7580  resqrexlemdecn  11196  summodclem2  11566  isumss2  11577  pcdvdstr  12523  ennnfoneleminc  12655  prdssgrpd  13119  prdsmndd  13152  grprcan  13241  mulgnn0dir  13360  mulgdir  13362  mulgass  13367  lmodprop2d  13982  lssintclm  14018  psrbaglesuppg  14304  restopnb  14503  blsscls2  14815