reserve X,Y,Z,X1,X2,X3,X4,X5,X6 for set, x,y for object;
reserve a,b,c for object, X,Y,Z,x,y,z for set;
reserve A,B,C,D for Ordinal;

theorem Th22:
  not ex X st for A holds A in X
proof
  defpred P[object] means $1 is Ordinal;
  given X such that
A1: A in X;
  consider Y such that
A2: for a being object holds a in Y iff a in X & P[a] from XBOOLE_0:sch 1;
  for x st x is Ordinal holds x in Y by A1,A2;
  then x in Y iff x is Ordinal by A2;
  hence contradiction by Th21;
end;
