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
  dom [:X,Y:] c= X
proof
  let x be object;
  assume x in dom [:X,Y:];
  then ex y being object st [x,y] in [:X,Y:] by XTUPLE_0:def 12;
  hence thesis by ZFMISC_1:87;
end;
