let A, B, x be set ; :: thesis: ( x in B implies A --> x is Function of A,B )
A1: rng (A --> x) c= {x} by Th13;
A2: dom (A --> x) = A by Th13;
assume A3: x in B ; :: thesis: A --> x is Function of A,B
then {x} c= B by ZFMISC_1:31;
then rng (A --> x) c= B by A1;
hence A --> x is Function of A,B by A3, A2, FUNCT_2:def 1, RELSET_1:4; :: thesis: verum