Halliday & Matthiessen (2014: 95):
The thematic equative actually realises two distinct semantic features, which happen to correspond to the two senses of the word identify. On the one hand, it identifies (specifies) what the Theme is; on the other hand, it identifies it (equates it) with the Rheme. The second of these features adds a semantic component of exclusiveness: the meaning is ‘this and this alone’.