  We find conditions on a function space $\bf{L}$ that ensure that it behaves
as an $L_p$-space in the sense that any unconditional basis of a complemented
subspace of $\bf{L}$ either is equivalent to the unit vector system of $\ell_2$
or has a subbasis equivalent to a disjointly supported basic sequence. This
dichotomy allows us to classify the symmetric basic sequences of $\bf{L}$.
Several applications to Orlicz function spaces are provided.
