I am little doubtful about "true". Even if "anything -> true" is always true, "true" is a literal / constant value in logic, can we "imply" it? A proposition can be true or false, but true / false, taken alone, are not propositions.
Q, (P V Q) and (~Q V P) are propositions. Are true and false propositions? If yes, then ok. If not, then how can we logically imply some thing which is not even a proposition !