The Constitution says that in cases of impeachment, "the party convicted shall nevertheless be liable and subject to indictment, trial, judgment and punishment, according to law." It does not except the president. But what impeachable offenses aren't covered by the new doctrine of immunity?
And "according to Law" here is a constitutional term of art meaning that statutory law controls. I.e. whether there is a presidential exception is for Congress, not the court, to decide.
