reserve X,Y for set;
reserve G for Group;
reserve n for Nat;

theorem Th5:
  for f being Element of SymGroup(X) holds f is Permutation of X
  proof
    let f be Element of SymGroup(X);
    the carrier of SymGroup(X) = permutations(X) by Def2;
    hence thesis by Th1;
  end;
