 Let \((\bT_a)_{a\in{\cO}}\) be a progression using the uniform reflection principle with PA as the base theory T. Then we have: for any true arithmetical sentence F there is an \(a\in{\cO}\), such that \(\bT_a\vdash F\). Moreover, \(a\in{\cO}\) can be chosen such that \({{\mid}\,{a}\,{\mid}}\leq \omega^{\omega^{\omega+1}}\).