reserve A,B,X,X1,Y,Y1,Y2,Z for set, a,x,y,z for object;
reserve P,R for Relation of X,Y;

theorem
  R|X1 is Relation of X1,Y
proof
  now
    let x,y be object;
    assume [x,y] in R|X1;
    then x in X1 & y in Y by RELAT_1:def 11,ZFMISC_1:87;
    hence [x,y] in [:X1,Y:] by ZFMISC_1:87;
  end;
  hence thesis by RELAT_1:def 3;
end;
