reserve x,y for object;
reserve S for non void non empty ManySortedSign,
  o for OperSymbol of S,
  U0,U1, U2 for MSAlgebra over S;

theorem Th9:
  for U1,U2 be MSSubAlgebra of U0 st the Sorts of U1 = the
  Sorts of U2 holds the MSAlgebra of U1 = the MSAlgebra of U2
proof
  let U1,U2 be MSSubAlgebra of U0;
  assume the Sorts of U1 = the Sorts of U2;
  then U1 is MSSubAlgebra of U2 & U2 is MSSubAlgebra of U1 by Th8;
  hence thesis by Th7;
end;
