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 Th70:
  P c= R implies P|X c= R|X
proof
  assume
A1: P c= R;
  let x,y;
  assume [x,y] in P|X;
  then [x,y] in P & x in X by Def9;
  hence thesis by A1,Def9;
end;
