Why do we require that $1 \in A$ in defining n-admissible functions?

Question

In the proof of the Iteration Theorem in Eliot Mendelson's book Number Systems and the Foundations of Analysis (1973), page 57, the author defines a function $f: A \to W$ to be n-admissible iff:

1. $A \subseteq P$
2. $1 \in A$
3. $n \in A$
4. $\forall u (S(u) \in A \implies u \in A)$
5. $f(1) = c$
6. $\forall u (S(u) \in A \implies f(S(u)) = g(f(u))).$

I don't see why we need (2). Do (3) and (4) not imply that $1 \in A$?