reserve S for non empty non void ManySortedSign,
  A for MSAlgebra over S;
reserve A for non-empty MSAlgebra over S;
reserve S for non empty non void ManySortedSign,
  A for non-empty MSAlgebra over S,
  R for ManySortedRelation of the Sorts of A;

theorem
  for R being ManySortedRelation of A holds EqTh R = EqCl(TRS R,A)
proof
  let R be ManySortedRelation of A;
A1: TRS R c= EqCl(TRS R,A) by Th43;
  R c= TRS R by Def13;
  then R c= EqCl(TRS R,A) by A1,PBOOLE:13;
  then
A2: EqTh R c= EqCl(TRS R,A) by Def15;
  R c= EqTh R by Def15;
  then TRS R c= EqTh R by Def13;
  then EqCl(TRS R,A) c= EqTh R by Th44;
 hence thesis by A2,PBOOLE:146;
end;
