I think your "exists x" inside parentheses in the last two steps are typos (or if not.. then they are mistakes).
How about
?
Exercise 1(e) in Section 2.2 of Daniel Velleman's How to prove it:
Negate the statement and then reexpress the result as an equivalent positive statement:
My attempt at the solution is by expressing it in the logical form as
Step 1:
Step 2: negate the statement
Question: Is there a set notation that is equivalent to the last line?