  The functional delta-method provides a convenient tool for deriving the
asymptotic distribution of a plug-in estimator of a statistical functional from
the asymptotic distribution of the respective empirical process. Moreover, it
provides a tool to derive bootstrap consistency for plug-in estimators from
bootstrap consistency of empirical processes. It has recently been shown that
the range of applications of the functional delta-method for the asymptotic
distribution can be considerably enlarged by employing the notion of
quasi-Hadamard differentiability. Here we show in a general setting that this
enlargement carries over to the bootstrap. That is, for quasi-Hadamard
differentiable functionals bootstrap consistency of the plug-in estimator
follows from bootstrap consistency of the respective empirical process. This
enlargement often requires convergence in distribution of the bootstrapped
empirical process w.r.t.\ a nonuniform sup-norm. The latter is not problematic
as will be illustrated by means of examples.
