  In this paper we exploit the notions of conjoined and iterated conditionals,
which are defined in the setting of coherence by means of suitable conditional
random quantities with values in the interval $[0,1]$. We examine the iterated
conditional $(B|K)|(A|H)$, by showing that $A|H$ p-entails $B|K$ if and only if
$(B|K)|(A|H) = 1$. Then, we show that a p-consistent family
$\mathcal{F}=\{E_1|H_1,E_2|H_2\}$ p-entails a conditional event $E_3|H_3$ if
and only if $E_3|H_3=1$, or $(E_3|H_3)|QC(\mathcal{S})=1$ for some nonempty
subset $\mathcal{S}$ of $\mathcal{F}$, where $QC(\mathcal{S})$ is the quasi
conjunction of the conditional events in $\mathcal{S}$. Then, we examine the
inference rules $And$, $Cut$, $Cautious $ $Monotonicity$, and $Or$ of System~P
and other well known inference rules ($Modus$ $Ponens$, $Modus$ $Tollens$,
$Bayes$). We also show that $QC(\mathcal{F})|\mathcal{C}(\mathcal{F})=1$, where
$\mathcal{C}(\mathcal{F})$ is the conjunction of the conditional events in
$\mathcal{F}$. We characterize p-entailment by showing that $\mathcal{F}$
p-entails $E_3|H_3$ if and only if $(E_3|H_3)|\mathcal{C}(\mathcal{F})=1$.
Finally, we examine \emph{Denial of the antecedent} and \emph{Affirmation of
the consequent}, where the p-entailment of $(E_3|H_3)$ from $\mathcal{F}$ does
not hold, by showing that $(E_3|H_3)|\mathcal{C}(\mathcal{F})\neq1.$

Probability;Logic