Theorem sselda

Description: Membership deduction from subclass relationship. (Contributed by NM, 26-Jun-2014)

	Ref	Expression
Hypothesis	sseld.1	$$⊢\phi \to A\subseteq B$$
Assertion	sselda	$$⊢\left(\phi \wedge C\in A\right)\to C\in B$$

Proof

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