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
  X c= X1 & Y c= Y1 implies R is Relation of X1,Y1
proof
  assume X c= X1 & Y c= Y1;
  then [:X,Y:] c= [:X1,Y1:] by ZFMISC_1:96;
  hence thesis by XBOOLE_1:1;
end;
