reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     :: ZFMISC_1:26
  {x,y} c= {A} implies x = A & y = A
proof
  assume
A1: {x,y} c= {A};
  now
    let i be object;
    assume
A2: i in I;
    then {x,y}.i c= {A}.i by A1;
    then {x,y}.i c= {A.i} by A2,Def1;
    then {x.i,y.i} c= {A.i} by A2,Def2;
    hence x.i = A.i by ZFMISC_1:20;
  end;
  hence x = A;
  now
    let i be object;
    assume
A3: i in I;
    then {x,y}.i c= {A}.i by A1;
    then {x,y}.i c= {A.i} by A3,Def1;
    then {x.i,y.i} c= {A.i} by A3,Def2;
    hence y.i = A.i by ZFMISC_1:20;
  end;
  hence thesis;
end;
