Rational Pavelka predicate logic is a conservative extension of Lukasiewicz predicate logic

Rational Pavelka logic extends Lukasiewicz infinitely valued logic by addin g truth constants for rationals in [0, 1]. We show that this is a conservat ive extension. We note that this shows that provability degree can be defin ed in Lukasiewicz logic, we also give a counterexample to a soundness theor em of Belluce and Chang published in 1963.