database - Proving FD's on a set of relations- Need solution checked

Question

I am having issues proving functional dependencies with Armstrong's Axioms. I am struggling with this:

Let R(A,B,C,D,E) be a relation schema and F = {A→CD, C→E, B→D}

Prove: F: BC-> DE

What I have:

1. Given B->D
2. Augment C on 1, BC -> DC
3. Decomposition on 2, BC -> D, BC -> C
4. Transitivity on BC -> C, BC -> E
5. Union on BC -> D and 4, BC -> DE

Unsure if this is a proper solution.

Answer 1

You are absolutely right my friend. Your Proof is flawless.