reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;
reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for Element of X;

theorem
  for X,Y,A being set, z being set st z in A & A c= [:X,Y:] ex x
  being Element of X, y being Element of Y st z = [x,y]
proof
  let X,Y,A be set, z be set;
  assume z in A & A c= [:X,Y:];
  then consider x,y being object such that
A1: x in X and
A2: y in Y and
A3: z = [x,y] by ZFMISC_1:84;
  reconsider x,y as set by TARSKI:1;
  reconsider y as Element of Y by A2,Def1;
  reconsider x as Element of X by A1,Def1;
  take x,y;
  thus thesis by A3;
end;
