Theorem ss2in

Description: Intersection of subclasses. (Contributed by NM, 5-May-2000)

	Ref	Expression
Assertion	ss2in	$$⊢\left(A\subseteq B\wedge C\subseteq D\right)\to A\cap C\subseteq B\cap D$$

Proof

Step	Hyp	Ref	Expression
1		ssrin	$$⊢A\subseteq B\to A\cap C\subseteq B\cap C$$
2		sslin	$$⊢C\subseteq D\to B\cap C\subseteq B\cap D$$
3	1 2	sylan9ss	$$⊢\left(A\subseteq B\wedge C\subseteq D\right)\to A\cap C\subseteq B\cap D$$