 This principle is not without consequence. Since \(Px \rightarrow Px\) is a tautology, the combination with modus ponens and existential generalization yields \(\exists x(Px \rightarrow Px)\) as a theorem. For another example, consider the theorem \(\forall xPx \rightarrow \exists xPx\), which is similarly derivable from the axioms by combining universal instantiation and existential generalization. Some have found these consequences objectionable on the grounds that the existence of an object should not be derivable from logic alone.