Theorem 3-5. If $a_1,a_2,\ldots,a_m$ is a complete residue system $\pmod m$ and $\gcd(k,m)=1$, then $ka_1,ka_2,\ldots,ka_m$ also is a complete residue system $\pmod m$
Proof: We show directly that properties (a) and (b) below hold for this new set
A set $a_1,\ldots,a_m$ called a complete residue system modulo $m$, is characterized by the following properties.
a) if $i \neq j$, then $a_i \not\equiv a_j \pmod m$
b) If a is any integer, there is an index i with $1 \leq i \leq m$ for which $a\equiv a_i\pmod m$
I am having troubles understanding property b
b_) Theorem 2-6 shows that of $(k,m)=1$, the congruence $kx \equiv a \pmod m$ has a solution for any fixed $a$. Let a solution be $x_0$. Since $a_1,\ldots,a_m$ is a complete residue system, there is an index $i$ such that $x_0 \equiv a_i\pmod m$. Hence $kx_0 \equiv ka_i \equiv a \pmod m$.
The book mentions the existence of a theorem 2-6, but it doesn't exists, so I need an explanation about it.