Express the quantification:

Question

Existential(!)x P(x)

using universal quantifications, existential quantification and logical expressions. For sake of typing this question, I'm going to let "E" be the existential quantifier, "A" be the universal quantifier", and "^" means "and":

so far I have:

Ex(P(x) ^ Ay --> P(y))

But I have no idea if this is actually correct! I really appreciate your help!
Thanks!