theorem Th23:
  for z being Complex holds z-z*' = 2*(Im z) * <i>
proof
  let z be Complex;
  z-z*'= Re z - Re (z*') + (Im z - Im (z*'))*<i> by COMPLEX1:84
    .= Re z - Re (z*')+(Im z - -Im z)*<i> by COMPLEX1:27
    .= Re z - Re z + (Im z - -Im z)*<i> by COMPLEX1:27
    .= 2*(Im z)*<i>;
  hence thesis;
end;
