  A key feature of the Trappist-1 system is its monotonic decrease in bulk
density with growing distance from the central star, which indicates an ice
mass fraction that is zero in the innermost planets, b and c, and about 10\% in
planets d through h. Previous studies suggest that the density gradient of this
system could be due to the growth of planets from icy planetesimals that
progressively lost their volatile content during their inward drift through the
protoplanetary disk. Here we investigate the alternative possibility that the
planets formed in a dry protoplanetary disk populated with pebbles made of
phyllosilicates, a class of hydrated minerals with a water fraction possibly
exceeding 10 wt\%. We show that the dehydration of these minerals in the inner
regions of the disk and the outward diffusion of the released vapor up to the
ice-line location allow the condensation of ice onto grains. Pebbles with water
mass fractions consistent with those of planets d--h would have formed at the
snow-line location. In contrast, planets b and c would have been accreted from
drier material in regions closer to the star than the phyllosilicate
dehydration line.
