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  7314  prarloclemlt  7553  prarloclemlo  7554  resqrexlemdecn  11156  summodclem2  11525  isumss2  11536  pcdvdstr  12465  ennnfoneleminc  12568  grprcan  13109  mulgnn0dir  13222  mulgdir  13224  mulgass  13229  lmodprop2d  13844  lssintclm  13880  psrbaglesuppg  14158  restopnb  14349  blsscls2  14661