
theorem
  for x,y,z being Element of BOOLEAN holds and3.<*x,y,z*> = x '&' y '&'
z & and3a.<*x,y,z*> = 'not' x '&' y '&' z & and3b.<*x,y,z*> = 'not' x '&' 'not'
  y '&' z & nor3.<*x,y,z*> = 'not' x '&' 'not' y '&' 'not' z by Def9,Def10
