(related to Proposition: Intersection of a Set With Another Set is Subset of This Set)
- Let $A$ and $B$ be sets.
- Let $A\cap B$ be the intersection of $A$ and $B$.
- We will prove $A\cap B\subseteq A$. The proof for $A\cap B\subseteq B$ is similar.
- Since $x\in A$ for all $x\in A\cap B$, then by definition of subset $A\cap B\subseteq A$.
Thank you to the contributors under CC BY-SA 4.0!
- Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016