Full Idea
We shall use 'a=b' as short for 'a is the same thing as b'. The sign '=' thus expresses a particular two-place predicate. Officially we will use 'I' as the identity predicate, so that 'Iab' is as formula, but we normally 'abbreviate' this to 'a=b'.
Gist of Idea
The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b)
Source
David Bostock (Intermediate Logic [1997], 8.1)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.323