  Modus ponens (\emph{from $A$ and "if $A$ then $C$" infer $C$}, short: MP) is
one of the most basic inference rules. The probabilistic MP allows for managing
uncertainty by transmitting assigned uncertainties from the premises to the
conclusion (i.e., from $P(A)$ and $P(C|A)$ infer $P(C)$). In this paper, we
generalize the probabilistic MP by replacing $A$ by the conditional event
$A|H$. The resulting inference rule involves iterated conditionals (formalized
by conditional random quantities) and propagates previsions from the premises
to the conclusion. Interestingly, the propagation rules for the lower and the
upper bounds on the conclusion of the generalized probabilistic MP coincide
with the respective bounds on the conclusion for the (non-nested) probabilistic
MP.
