Theorem ssinss1

Description: Intersection preserves subclass relationship. (Contributed by NM, 14-Sep-1999) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

	Ref	Expression
Assertion	ssinss1	$$⊢A\subseteq C\to A\cap B\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		ssrin	$$⊢A\subseteq C\to A\cap B\subseteq C\cap B$$
2		inss1	$$⊢C\cap B\subseteq C$$
3	1 2	sstrdi	$$⊢A\subseteq C\to A\cap B\subseteq C$$