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
  a 'nand' (a '&' b) = a 'nand' b
proof
  a 'nand' (a '&' b) = (a '&' a) 'nand' b by Th10;
  hence thesis;
end;
