A Symbolic Reachability Graph (SRG) is a highly condensed representation of system state space built automatically from a specification of system in terms of Wellformed net. The building of such graph profits from the presence of object symmetries to aggregate either states or actions within symbolic representatives. In this paper, we show how to make operational the CTL* formal checking system presented in [1]. Our technique consists in exploiting the SRG by taking into account the object symmetries only if they leave the formula invariant. The difficulty to bypass is that SRG does not preserve explicitly the behavior of the objects specified within formulas. This leads to a new specification of system, from which we can prove that model checking through a state space is equivalent to model checking through the symbolic reachability graph.