reserve a,b,c,d for Ordinal;
reserve l for non empty limit_ordinal Ordinal;
reserve u for Element of l;
reserve A for non empty Ordinal;
reserve e for Element of A;
reserve X,Y,x,y,z for set;
reserve n,m for Nat;

theorem Th1:
  X is ordinal-membered iff for x st x in X holds x is ordinal
  proof
    thus X is ordinal-membered implies for x st x in X holds x is ordinal;
    assume
A1: for x st x in X holds x is ordinal;
    take a = sup X;
    let x be object; assume
A2: x in X; then
    x is Ordinal by A1;
    hence thesis by A2,ORDINAL2:19;
end;
