 In contemporary systems of logic an axiom or rule of inference allows that if \(x = y\), then for any predicate \(\phi\), \(\phi x \equiv \phi y\). In other words, identicals are indiscernible. The given definition of identity only suffices if it is not possible that entities x and y which share all predicative properties, cannot be distinguished by some property of a higher order. The axiom of reducibility guarantees that x and y sharing properties of any given higher order will entail sharing predicative properties, and so by the definition of identity, \(x = y\).