reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem
  R c= S iff R c= S|dom R
proof
 thus R c= S implies R c= S|dom R
  proof
   assume R c= S;
    then R|dom R c= S|dom R by Th70;
   hence thesis;
  end;
 thus thesis by Def9;
end;
