 reserve x,y,z,t for object,X,Y,Z,W for set;
 reserve R,S,T for Relation;

theorem Th3:
  R c= [:X,Y:] implies dom R c= X & rng R c= Y
proof
  assume R c= [:X,Y:];
  then R /\ [:X,Y:] = R by XBOOLE_1:28;
  hence thesis by Th1;
end;
