reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;
reserve Y for non empty set,
  a,b,c for Function of Y,BOOLEAN;

theorem Th10:
  a 'nand' (b '&' c) = (a '&' b) 'nand' c
proof
  (a '&' b) 'nand' c = 'not' (a '&' b '&' c) by th1;
  hence thesis by Th9;
end;
