User blog comment:MilkyWay90/Help understand the zeta ordinals/@comment-5529393-20180620055127/@comment-32697988-20180621053054

Yes. And \(\phi(4,\alpha)=\eta_{\phi(4,\alpha)}\), \(\phi(5,\alpha)=\phi(4,\phi(5,\alpha))\), \(\phi(6,\alpha)=\phi(5,\phi(6,\alpha))\), etc.