For all x, for all y, if x is the same thing as y, then for any property P, x has property P if and only if Y has property P.

In other words, if M is the same thing as B, then whatever is true of M is true of B--and vice versa.

So, if my thought that the paper is due soon is identical to some state of my brain, then whatever is true of that thought is true of that brainstate, and whatever is true of the brainstate is true of the thought.