reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem
 for x1,x2,y1,y2 being object holds
  x1 <> x2 implies rng((x1,x2) --> (y1,y2)) = {y1,y2}
proof let x1,x2,y1,y2 be object;
  set h = (x1,x2) --> (y1,y2);
  assume
A1: x1 <> x2;
  thus rng h c= {y1,y2} by Th62;
  let y be object;
  assume y in {y1,y2};
  then y = y1 or y = y2 by TARSKI:def 2;
  then
A2: h.x1 = y or h.x2 = y by A1,Th63;
  dom h = {x1,x2} by Th62;
  then x1 in dom h & x2 in dom h by TARSKI:def 2;
  hence thesis by A2,FUNCT_1:def 3;
end;
