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Service network graph (SNG) was proposed as a network service sharing infrastructure to support secure services on dynamic aggregation of heterogeneous networks. To participate in SNG, a network has to share a secret key with one member of the SNG. The shared secret key will be used to set up an encrypted channel between the network and the SNG member. It is imperative to authenticate the data sent through the encrypted channel. This paper uses the symbols and approached presented by Lampson in his paper to provide a formal proof of how encryption channel authenticates itself in SNG. It forms the basis of using encrypted channels in SNG.