Theorem nfii1

Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by NM, 15-Oct-2003)

	Ref	Expression
Assertion	nfii1	$$⊢\underset{\_}{Ⅎ}x\bigcap _{x\in A}B$$

Proof

Step	Hyp	Ref	Expression
1		df-iin	$$⊢\bigcap _{x\in A}B=\left\{y|\forall x\in Ay\in B\right\}$$
2		nfra1	$$⊢Ⅎx\forall x\in Ay\in B$$
3	2	nfab	$$⊢\underset{\_}{Ⅎ}x\left\{y|\forall x\in Ay\in B\right\}$$
4	1 3	nfcxfr	$$⊢\underset{\_}{Ⅎ}x\bigcap _{x\in A}B$$