reserve a for set,
  i for Nat;
reserve MS for segmental non void 1-element ManySortedSign,
  A for non-empty MSAlgebra over MS;

theorem Th20:
  for B being non-empty MSSubAlgebra of A holds 1-Alg B is
  SubAlgebra of 1-Alg A
proof
  let B be non-empty MSSubAlgebra of A;
  the carrier of 1-Alg B is Subset of 1-Alg A & for S being non empty
Subset of 1-Alg A st S = the carrier of 1-Alg B holds the charact of(1-Alg B) =
  Opers( 1-Alg A,S) & S is opers_closed by Th17,Th18,Th19;
  hence thesis by UNIALG_2:def 7;
end;
