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 Th62:
 for x1,x2,y1,y2 being object holds
  dom((x1,x2) --> (y1,y2)) = {x1,x2} & rng((x1,x2) --> (y1,y2)) c= {y1,y2}
proof let x1,x2,y1,y2 be object;
  set f = {x1} --> y1, g = {x2} -->y2, h = (x1,x2) --> (y1,y2);
  rng f \/ rng g c= {y1} \/ {y2} by XBOOLE_1:13;
  then
A1: rng f \/ rng g c= {y1,y2} by ENUMSET1:1;
  dom f \/ dom g = {x1,x2} by ENUMSET1:1;
  hence dom h = {x1,x2} by Def1;
  rng h c= rng f \/ rng g by Th17;
  hence thesis by A1;
end;
