
theorem
  for x,y,z being Element of BOOLEAN holds nand3.<*x,y,z*>='not' (x '&'
  y '&' z) & nand3a.<*x,y,z*>='not' ('not' x '&' y '&' z) & nand3b.<*x,y,z*>=
'not' ('not' x '&' 'not' y '&' z) & or3.<*x,y,z*>='not' ('not' x '&' 'not' y
  '&' 'not' z) by Def12,Def13,Def14,Lm5;
