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' (b 'nand' c) = 'not' a 'or' (b '&' c) & a 'nand' (b 'nand' c)
  = a 'imp' (b '&' c)
proof
  a 'nand' (b 'nand' c) = 'not' (a '&' (b 'nand' c)) by th1
    .= 'not' (a '&' 'not' (b '&' c)) by th1
    .= 'not' a 'or' 'not' 'not' (b '&' c) by BVFUNC_1:14
    .= 'not' a 'or' (b '&' c);
  hence thesis by BVFUNC_4:8;
end;
