when knowledge de dicto implies knowledge de re.

Suppose that Angela believes that Santa Clause exists. One way to think of Angela’s belief is in terms of a relationship between Angela and a certain proposition, as in the following expression:  

B_a((∃x)x = Santa Clause))

i.e.—Angela believes that there is something such that it is Santa Clause.

Another way to think of Angela’s belief is in terms of a relationship between Angela and a thing, as in:  

(∃x)B_a(x = Santa Clause)

i.e. There is something such that Angela believes that it is Santa Clause.

Notice that first expression implies the existence of Angela but nothing else. The second expression implies the existence of Angela and as well as the thing which Angela believes to be Santa Clause. (Even if there is no such thing as Santa Clause, the second expression asserts that there is at least one thing which bears the relation of being believed to be Santa Clause by Angela).

Notice that this difference between these expressions disappears if the relation in question is not belief but knowledge. Consider:

K_a((∃x)x = Santa Clause))

i.e.—Angela knows that there is something such that it is Santa Clause. And

(∃x)K_a(x = Santa Clause)

i.e.—There is something such Angela knows that it is Santa Clause.

Regarding the latter expression: If there is something such that Angela knows that it is Santa Clause, then both Angela and Santa Clause exist. And the same goes for the latter expression: Angela knows that there is something such that it is Santa Clause only if Angela exists and her  belief is true, and her belief that there is something such that it is Santa Clause is true only if—you guessed it—there is something such that is Santa Clause. Generalizing, this latter point underwrites the following inference rule of epistemic logic:

          K_m((∃x)(φx))

    ∴ (∃x)(φx)