 Another example of the same kind is the following: the algebraic fibring between the logic of classical negation \(\neg\) and the logic of classical implication \(\to\) regarded in the categories above does not recover classical logic expressed over \(\neg\) and \(\to\). Indeed, the resulting logic system, defined over \(\neg\) and \(\to\), cannot validate Ex Contradictione Sequitur Quodlibet when presented as an axiom:   \[\not\vdash(\varphi \to(\neg\varphi \to \psi)).\]   