Theorem sselii

Description: Membership inference from subclass relationship. (Contributed by NM, 31-May-1999)

	Ref	Expression
Hypotheses	sseli.1	$$⊢A\subseteq B$$
	sselii.2	$$⊢C\in A$$
Assertion	sselii	$$⊢C\in B$$

Proof

Step	Hyp	Ref	Expression
1		sseli.1	$$⊢A\subseteq B$$
2		sselii.2	$$⊢C\in A$$
3	1	sseli	$$⊢C\in A\to C\in B$$
4	2 3	ax-mp	$$⊢C\in B$$