Theorem simplr3 1065

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 1029	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1002

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 1004

This theorem is referenced by:  netap  7456  prarloclemlt  7696  prarloclemlo  7697  ccatswrd  11223  pfxccat3  11287  resqrexlemdecn  11544  summodclem2  11914  isumss2  11925  pcdvdstr  12871  ennnfoneleminc  13003  prdssgrpd  13469  prdsmndd  13502  grprcan  13591  mulgnn0dir  13710  mulgdir  13712  mulgass  13717  lmodprop2d  14333  lssintclm  14369  psrbaglesuppg  14657  restopnb  14876  blsscls2  15188