Theorem sseldd

Description: Membership inference from subclass relationship. (Contributed by NM, 14-Dec-2004)

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

Proof

Step	Hyp	Ref	Expression
1		sseld.1	$$⊢\phi \to A\subseteq B$$
2		sseldd.2	$$⊢\phi \to C\in A$$
3	1	sseld	$$⊢\phi \to \left(C\in A\to C\in B\right)$$
4	2 3	mpd	$$⊢\phi \to C\in B$$