reserve S,S9 for non void Signature,
  f,g for Function;

theorem
  for S being Signature, E being Extension of S, A being Algebra of E
  holds A is Algebra of S
proof
  let S be Signature, E be Extension of S, A be Algebra of E;
  consider E9 be non void Extension of E such that
A1: A is feasible MSAlgebra over E9 by Def7;
  E9 is Extension of S by Th46;
  hence thesis by A1,Def7;
end;
