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 Th54:
  a 'imp' (b 'nand' c) = 'not' (a '&' b '&' c)
proof
  thus a 'imp' (b 'nand' c) =a 'imp' 'not' (b '&' c) by th1
    .='not' a 'or' 'not' (b '&' c) by BVFUNC_4:8
    .='not' (a '&' (b '&' c)) by BVFUNC_1:14
    .='not' (a '&' b '&' c) by BVFUNC_1:4;
end;
