Prove that AD->B using armstrong's axioms

Question

R(A,B,C,D) F={A->C, D->B}

using Armstrong's axioms how do I prove that AD->B?

what I currently have is: using augmentation if D->B and A is any subset of U, then AD->AB but I'm not confident on that answer

Answer 1

Here is a simple proof:

1. D -> B by hypothesis
2. AD -> AB by augmentation of 1
3. AB -> B by reflexivity
4. AD -> B by transitivity of 2 and 3