Wireless mesh networks are a combination of wireless local area network (LAN) and mobile ad hoc network, and they are of a new multi-hop network structure. The openness of wireless networks and the limitation of resources make wireless networks vulnerable to replay attack, impersonation attack, and so on. Logic of events is a formal method to describe the protocol state transition and algorithm in concurrent and distributed systems, which can be used to prove the security of network protocols. Based on the logic of events, we propose a series of properties that include multiple combinations of information interaction, no stacking, event matching, dereplication and remove future. We utilize these rules to reduce the redundancy and complexity of the protocol validation process, and improve protocol analysis efficiency. We study the bidirectional authentication protocol of wireless Mesh network clients, and conclude that the protocol can resist man-in-the-middle replay attacks. The mesh protocol is proved secure. The logic of events can be applied to the formal analysis and verification of similar complex wireless network protocols.