  As one can see, Frege didn’t use the primitive connectives ‘and’, ‘or’, or ‘if and only if’, but always used canonical equivalent forms defined in terms of negations and conditionals. Note the last row of the table — when Frege wants to assert that two conditions are materially equivalent, he uses the identity sign, since this says that they denote the same truth-value. In the modern sentential calculus, the biconditional does something equivalent, for a statement of the form \(\phi \equiv \psi\) is true whenever \(\phi\) and \(\psi\) are both true or both false. The only difference is, in the modern sentential calculus \(\phi\) and \(\psi\) are not construed as terms denoting truth-values, but rather as sentences having truth conditions. Of course, Frege could, in his notation, use the sentence ‘\((\phi \to \psi) \amp (\psi \to \phi)\)’ to assert \(\phi \equiv \psi\).