With a new premise that reflection is essentially empty of any new ground or source of knowledge, we cannot accept all of the original three premises of dogmatic metaphysics. Since a division into mediate and immediate is logically exhaustive and we already accept that mediate knowledge, or reflection is empty, then there must be immediate knowledge which is not intuitive. This must actually mean that we are unconscious of the non-intuitive immediate ground. The knowledge itself is neither believed nor thought, as such, and it is not explicitly present to us as the table or chair is perceptually. This is ultimately an appeal to intuition, but in present time it is only an appeal to memory.
Demonstration is merely a showing of the obvious.
Where the obvious is no longer present or escapes the nature of our perceptions, then other considerations come into play. Deduction is a showing of the unobvious, but still importantly a showing. Deduction cannot logically prove the propositions in questions any more than the demonstration of an intuitive ground can. But the cognitive force of each is the same. The first questions about non-intuitive immediate knowledge would be how it comes to be consciously known, having been unconsciously known, and then how we know that it is what we think it is.