Theorem sseld

Description: Membership deduction from subclass relationship. (Contributed by NM, 15-Nov-1995)

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

Proof

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