Where you have your first ⇒ sign, you need to replace that with ∀x .

p ⇒ q can be thought of as "if p then q".

So, I'd say:

For any positive value of epsilon, there exists a positive number delta, such that for any x, IF the distance of x from c is less than delta (and greater than zero) THEN the distance of f(x) from L is less than epsilon.