All total functions form a PRC class
You cannot say that every total function is computable, since that is not true. For example, the function $f(n)$ which returns $1$ if the $n$'th Turing machine halts and $0$ otherwise is not computable.

However, the question is much simpler. The definition of a PRC class specifies several closure properties, of the form: if so-and-so belong to the class, then such-and-such also belongs to the class (these include the "axioms", in which the premise is empty). Since the class of all (total) functions contains all functions, it automatically satisfies these constraints.