 But if both \(c = \#P\) and \(c = \#Q\), then \(\#P = \#Q\). So, by Hume’s Principle, \(P \approx Q\). So, by the Equinumerosity Lemma, it follows that \(P^{-d} \approx Q^{-e}\). If so, then by Hume’s Principle, \(\#P^{-d} = \#Q^{-e}\). But then, \(a = b\).