I have always seen in classes at university theorems, proofs, corrollaries etc... stating that, for example, that there $\exists b\in \mathbb{N}$ such that b is unique. However, after taking this course which taught us a lot about writing this in mathematical terms, I was wondering how would you formally write that a term is unique.
Example: $∀a,n∈N,\exists b\in \mathbb N, b < n \land ab \equiv_n 1.$ How would you add to this statement that not only $b$ exists but $b$ is unique? Other than just putting ∃!?