theorem Th45:
  x in B implies A --> x is Function of A,B
proof
A1: rng (A --> x) c= {x} by Th13;
A2: dom (A --> x) = A;
  assume
A3: x in B;
  then {x} c= B by ZFMISC_1:31;
  then rng (A --> x) c= B by A1;
  hence thesis by A3,A2,FUNCT_2:def 1,RELSET_1:4;
end;
