  We prove a noncommutative variant of Saskin's classical theorem -- on the
connection between Choquet boundaries for function spaces and Korovkin sets --
for operator systems generating separable Type I C*-algebras. The main result
implies an affirmative answer to a weaker version of Arveson's hyperrigidity
conjecture for such C*-algebras. It also yields information about the more
general version of Arveson's conjecture.
