 The implicit nature of the truth-definition is seen from the fact that the predicate \(\TRUE\) appears on both sides of the equivalence sign in these  clauses.[57]  The above implicit truth-definition of \(\mathbf{FO}\) for \(N\) is of the form ‘there is a set \(S\) interpreting the predicate \(\TRUE\) such that \(\psi(x)\).’ Thus the implicit truth-definition of \(\mathbf{FO}\) in \(\mathbf{FO}\) gives rise to the explicit truth-definition \(\exists \TRUE\, \psi(x)\) of \(\mathbf{FO}[\tau]\) in \(\mathbf{ESO}[\tau]\) for \(N\). Since \(\mathbf{ESO}\) and \(\mathbf{IFL}\) have the same expressive power, a truth-predicate of \(\mathbf{FO}\) for \(N\) can be formulated in \(\mathbf{IFL}\). 