Time hierarchy theorem to show $Time(n^7)$ strictly contained in P

Question

I'm relatively new to computational complexity and am trying to use the time hierarchy theorem to show that $Time(n^7)$ is strictly contained in P. I understand that the time hierarchy theorem says that if the limit as n tends to infinity of $\frac{T_1(n)}{T_2(n)}=0$ then $Time(T_1(n))$ is strictly contained in $Time(T_2(n))^2$. It seems obvious to me that this implies the desired result because for any number $x$ greater than 7, $Time(n^7)$ will be strictly contained in $Time(n^{2x})$ and then P is the union over all such time complexity classes. Could anyone help with how I might write this more formally? I feel like I might be missing something because it just seems clear to me, any help is much appreciated.