reserve f,g,h for Function,
  A for set;
reserve F for Function,
  B,x,y,y1,y2,z for set;
reserve x,z for object;

theorem
  not x in B implies (A --> x)"B = {}
proof
  assume
A1: not x in B;
  rng (A --> x) c= {x} by Th13;
  then rng (A --> x) misses B by A1,XBOOLE_1:63,ZFMISC_1:50;
  hence thesis by RELAT_1:138;
end;
