Relational Algebra: existential quantifiers

So i have the following question and template answer:

Question: List the names of managers who have at least one dependant.

Answer: {e.Fname, e.Lname | EMPLOYEE(e) AND (∃d)(∃t)(DEPARTMENT(d) AND DEPENDANT(t) AND e.Ssn = d.Mgrssn AND t.Essn = e.Ssn) }

My answer was exactly the same except that instead of the (∃d)(∃t)(…) section I said (∃d)(DEPARTMENT(d) AND e.Ssn = d.Mgrssn) AND (∃t)(DEPENDANT(t) AND t.Essn = e.Ssn).

My question is basically are these equivalent?