reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem Th81:
  a in con_class b iff a,b are_conjugated
proof
  thus a in con_class b implies a,b are_conjugated
  proof
    assume a in con_class b;
    then ex c st a = c & b,c are_conjugated by Th80;
    hence thesis;
  end;
  assume a,b are_conjugated;
  hence thesis by Th80;
end;
