set T = the categorical_product of C1,C2;
consider D being strict category, P1 being Functor of D,C1, P2 being Functor of D,C2 such that
A2:
( the categorical_product of C1,C2 = [D,P1,P2] & P1 is covariant & P2 is covariant & D,P1,P2 is_product_of C1,C2 )
by Def18;
thus
pr2 (C1,C2) is covariant
by A2; verum