Theorem sselid

Description: Membership inference from subclass relationship. (Contributed by NM, 25-Jun-2014)

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

Proof

Step	Hyp	Ref	Expression
1		sseli.1	$$⊢A\subseteq B$$
2		sselid.2	$$⊢\phi \to C\in A$$
3	1	sseli	$$⊢C\in A\to C\in B$$
4	2 3	syl	$$⊢\phi \to C\in B$$