It does, insofar as you can express anything meaningful in an inconsistent system. A formal system being inconsistent implies being able to prove some statement

It does, insofar as you can express anything meaningful in an inconsistent system. A formal system being inconsistent implies being able to prove some statement A, and also its converse ~A. If both A and ~A are true, then we can prove that every other statement in this system is also true. A quick proof: 1. A 2. A v B 3. ~A & A v B 4. B We start with A. The union (logical-or) of true statement (here A) and any other statement (say B) is a true statement, thus A v B. Then we introduce another true statement, ~A, via logical-and to get ~A & (A v B), which simplifies (disjunctive syllogism) to just B. So we have proved B, but B was arbitrary. It could be anything, including the statement that x = y for x and y two ostensible non-equal numbers.