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.
Database Theory – Proving A->B,C then A->B and A->C Using Armstrong Axioms
database-theorydependenciesprimary-keyrelational-theoryunique-constraint
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Best Answer
Just two steps: you can use reflexivity for
B C -> Band then transitivity fromA -> B Cand the previous dependency. Analogous solution for the second case.