Theorem ssiin

Description: Subset theorem for an indexed intersection. (Contributed by NM, 15-Oct-2003)

	Ref	Expression
Assertion	ssiin	$$⊢C\subseteq \bigcap _{x\in A}B\leftrightarrow \forall x\in AC\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}xC$$
2	1	ssiinf	$$⊢C\subseteq \bigcap _{x\in A}B\leftrightarrow \forall x\in AC\subseteq B$$