Theorem sstri

Description: Subclass transitivity inference. (Contributed by NM, 5-May-2000)

	Ref	Expression
Hypotheses	sstri.1	$$⊢A\subseteq B$$
	sstri.2	$$⊢B\subseteq C$$
Assertion	sstri	$$⊢A\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		sstri.1	$$⊢A\subseteq B$$
2		sstri.2	$$⊢B\subseteq C$$
3		sstr2	$$⊢A\subseteq B\to \left(B\subseteq C\to A\subseteq C\right)$$
4	1 2 3	mp2	$$⊢A\subseteq C$$