reserve a for set,
  i for Nat;

theorem Th16:
  for U1,U2 being Universal_Algebra st MSAlg U1 is MSSubAlgebra of
  MSAlg U2 holds U1 is SubAlgebra of U2
proof
  let U1,U2 be Universal_Algebra;
  assume
A1: MSAlg U1 is MSSubAlgebra of MSAlg U2;
  hence the carrier of U1 is Subset of U2 by Th13;
  let B be non empty Subset of U2;
  assume B=the carrier of U1;
  hence thesis by A1,Th14,Th15;
end;
