Question 978498
You can do a proof by contradiction.


Step 1) Assume the opposite of the conclusion. Assume ~~D which is equivalent to D


Step 2) Since we have D, we can use D -> (B -> C) and modus ponens to get B -> C


Step 3) Use simplification to go from B & ~C to just B. You can also free up ~C as well


Step 4) Use B and B -> C to get C (modus ponens again)


Step 5) The ~C and C contradict one another. So the original assumption is not possible. Therefore, the opposite of the assumption (D) is the only possibility.


So that's one way we can prove that ~D is the conclusion.