Theorem ssinss1

Description: Intersection preserves subclass relationship. (Contributed by NM, 14-Sep-1999)

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

Proof

Step	Hyp	Ref	Expression
1		inss1	$$⊢A\cap B\subseteq A$$
2		sstr2	$$⊢A\cap B\subseteq A\to \left(A\subseteq C\to A\cap B\subseteq C\right)$$
3	1 2	ax-mp	$$⊢A\subseteq C\to A\cap B\subseteq C$$