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
  X c= Y implies
  for R being X-defined Relation holds R is Y-defined
  proof assume
A1: X c= Y;
    let R be X-defined Relation;
    dom R c= X by Def16;
    hence dom R c= Y by A1;
  end;
