 Given a set of conditional assertions \(\mathbf{K}\) of the type \(\phi \nc \psi\) one may be interested in investigating what other conditional assertions follow. The following two strategems lead to the same results. The first option is to intersect all preferential consequence relations \(\nc\) that extend \(\mathbf{K}\) (in the sense that the conditional assertions in \(\mathbf{K}\) hold for \(\nc\)) obtaining the Preferential Closure \(\nc^{\mathrm{P}}\) of \(\mathbf{K}\). The second option is to use the five defining properties of preferential consequence relations as deduction rules for syntactic units of the form \(\phi \nc \psi\). This way we obtain the deductive system P with its consequence relation \(\vdash^{\mathrm{P}}\) for which: 