Theorem simplr3 1068

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 1032	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1005

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 1007

This theorem is referenced by:  netap  7564  prarloclemlt  7804  prarloclemlo  7805  ccatswrd  11355  pfxccat3  11419  resqrexlemdecn  11690  summodclem2  12061  isumss2  12072  pcdvdstr  13018  ennnfoneleminc  13151  prdssgrpd  13617  prdsmndd  13650  grprcan  13739  mulgnn0dir  13858  mulgdir  13860  mulgass  13865  lmodprop2d  14483  lssintclm  14519  psrbaglesuppg  14808  restopnb  15033  blsscls2  15345