reserve a,b,c,d for set,
  D,X1,X2,X3,X4 for non empty set,
  x1,y1,z1 for Element of X1,
  x2 for Element of X2,
  x3 for Element of X3,
  x4 for Element of X4,
  A1,B1 for Subset of X1;

theorem
  a in [:X1,X2:] implies ex x1,x2 st a=[x1,x2]
proof
  assume a in [:X1,X2:];
  then consider x1,x2 being object such that
A1: x1 in X1 and
A2: x2 in X2 and
A3: a=[x1,x2] by ZFMISC_1:def 2;
  reconsider x2 as Element of X2 by A2;
  reconsider x1 as Element of X1 by A1;
  take x1,x2;
  thus thesis by A3;
end;
