How to prove “A->B,C then A->B and A->C” from Armstrong Axioms

Question

I know that this is true but I don't understand how to prove it.

The Problem:

Prove or disprove that if A->B,C, then A->B and A->C

This answer is similar but it does not prove the relation using Armstrong's axioms.

Answer 1

Just two steps: you can use reflexivity for B C -> B and then transitivity from A -> B C and the previous dependency. Analogous solution for the second case.