Validity of CTL formula $s_0 \models EG\ AF\ p$ in given model

Question

I have been learning Verification by model checking recently and I get the following question:

Is the CTL formula $s_{0} \models EG\ AF\ p$ valid in the following model?

I think it is incorrect because there is a deadlock or infinite loop about $s_0$ after the state is starting from $s_0$, which make it invalid under $EG\ AF\ $ condition.

Am I correct? How can I prove it (or give a counterexample)?