# Is data modeled by dirichlet process mixture exchangeable?

Consider DPM model: \begin{aligned} X_{i} | \phi_{i} & \sim F\left(x;\phi_{i}\right) \\ \phi_{1}, \phi_{2}, \cdots | & P \stackrel{iid}{\sim} P \\ P & \sim D P(\alpha G_0) \end{aligned}
It is well-known that $$\{\phi_{i}\}$$ is exchangeable and $$P$$ is a.s. discrete. In this model, is $$\{X_{i}\}$$ also exchangeable?If not, why some scholars still persue non-exchangeable $$\{\phi_{i}\}$$ modeled by some new process, and then still model $$\{X_{i}\}$$ using mixture?
Any help will be appreciated!