For all sets `A, B` and C, if `A sub B`, then `A nn C sub B nn C`.

Explanation

To prove that if \( A \subseteq B \), then \( A \cap C \subseteq B \cap C \), we will follow these steps:

### Step 1: Understand the Definitions
We start with the definitions of subsets and intersections. If \( A \subseteq B \), it means every element of \( A \) is also an element of \( B \). The intersection \( A \cap C \) consists of all elements that are in both \( A \) and \( C \).

**Hint:** Recall the definitions of subset and intersection to understand the relationships between the sets.

### Step 2: Take an Element from \( A \cap C \)
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