There is however a special thematic structure in which two or more elements within the clause are explicitly grouped together to form a single constituent of the thematic structure: typically functioning as Theme, but sometimes on the other hand as Rheme. This is a particular kind of clause, a THEMATIC EQUATIVE, which is a form of ʻidentifyingʼ clause. In a thematic equative, all the elements are organized into two constituents; these two are then linked by a relationship of identity, a kind of ʻequal signsʼ, expressed by some form of the verb 'be'.
- Halliday (1985), a pag.41

A thematic equative (which is sometimes called a ʻpseudo-cleft sentenceʼ in formal grammar) is simply an identifying clause with a thematic nominalization in it. Its function is to express the Theme – Rheme structure in such a way as to allow for the Theme to consist of any subset of the elements of the clause.
- Halliday (1985), a pag.43

The thematic equative actually realizes two distinct semantic features, which happen to correspond to the two senses of the word ʻidentifyʼ. 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 ʻthis and this aloneʼ. So the meaning of 'what the duke gave my aunt was the teapot' is something like ʻI am going to tell you about the duke’s gift to my aunt: it was that teapot – and nothing elseʼ. Contrast this with 'the duke gave my aunt that teapot', where the meaning is ʻI am going to tell you something about the duke: he gave my aunt that teapotʼ (whith no implication that he did not do other things as well).
- Halliday (1985), a pag.43