Fun with substitutional quantification

Stipulate that "x strongly believes p" iff x believes p and it is not the case that x believes not-p. Consider the argument:

1. For anything that Freddie believes, there is a possible world where Sally strongly believes it.
2. Freddie believes the negation of Sally's deepest held belief.
3. Therefore, there is a possible world where Sally strongly believes the negation of Sally's deepest held belief.

Isn't it fun to derive an impossibility from two propositions whose conjunction is possible?

We learn from this that if we are to read (1) substitutionally, we need a substitutional quantification in which we are only allowed to substitute names. In that case, (3) does not follow from (1) and (2), because if "Xyzzy" is the name of the negation of Sally's deepest held belief, then instead of (3) all we get to conclude is:

4. There is a possible world where Sally strongly believes Xyzzy.

But there is no contradiction here, because in the relevant possible world, Xyzzy isn't the negation of Sally's deepest held belief. But still, wasn't (1)-(3) fun?