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 Th12:
  a in b iff epsilon_a in epsilon_b
  proof
    b c/= a iff epsilon_b c/= epsilon_a by Th11;
    hence thesis by Th4;
  end;
