reserve X,Y,x,y for set;
reserve A for non empty Poset;
reserve a,a1,a2,a3,b,c for Element of A;
reserve S,T for Subset of A;

theorem Th5:
  for A being transitive antisymmetric RelStr for a1,a2,a3 being
  Element of A holds a1 < a2 & a2 < a3 implies a1 < a3
by Th3,Th4;
