What you're describing seems to come down to the identity

(((w ∨ c) → a) ↔ ((w → a) ∧ (c → a)))

That is, an implication whose antecedent is a disjunction is a conjunction of implications. On the other hand,

((a → (w ∨ c)) ↔ ((a → w) ∨ (a → c)))

That is, an implication whose consequent is a disjunction is a disjunction of implications.