Preimage of Union under Mapping

Theorem
Let $$f: S \to T$$ be a mapping. Let $$C$$ and $$D$$ be subsets of $$T$$. Then:

$$f^{-1} \left({C \cup D}\right) = f^{-1} \left({C}\right) \cup f^{-1} \left({D}\right)$$

Proof
As $$f$$, being a mapping, is also a relation, we can apply Preimage of Union:

$$\mathcal{R}^{-1} \left({C \cup D}\right) = \mathcal{R}^{-1} \left({C}\right) \cup \mathcal{R}^{-1} \left({D}\right)$$