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 Th69:
  X c= Y implies R|X c= R|Y
proof
  assume
A1: X c= Y;
  let x,y;
  assume [x,y] in R|X;
  then x in X & [x,y] in R by Def9;
  hence [x,y] in R|Y by A1,Def9;
end;
