  We introduce the notion of a $(\Pi,\lambda)$-structure on a C-system and show
that C-systems with $(\Pi,\lambda)$-structures are constructively equivalent to
contextual categories with products of families of types. We then show how to
construct $(\Pi,\lambda)$-structures on C-systems of the form $CC({\cal C},p)$
defined by a universe $p$ in a locally cartesian closed category $\cal C$ from
a simple pull-back square based on $p$. In the last section we prove a theorem
that asserts that our construction is functorial.
  This version introduces some changes compared to the previous one to ensure
rigorous compatibility with arXiv:1409.7925v3.
