
theorem Th1:
  for X, Y being set, D being Subset of [:X,Y:] holds D c= [:proj1 D, proj2 D:]
proof
  let X, Y be set, D be Subset of [:X,Y:];
  let q be object;
  assume
A1: q in D;
  then consider x, y being object such that
  x in X and
  y in Y and
A2: q = [x,y] by ZFMISC_1:def 2;
  x in proj1 D & y in proj2 D by A1,A2,XTUPLE_0:def 12,def 13;
  hence thesis by A2,ZFMISC_1:def 2;
end;
