Theorem nfiu1

Description: Bound-variable hypothesis builder for indexed union. (Contributed by NM, 12-Oct-2003)

	Ref	Expression
Assertion	nfiu1	$$⊢\underset{\_}{Ⅎ}x\bigcup _{x\in A}B$$

Proof

Step	Hyp	Ref	Expression
1		df-iun	$$⊢\bigcup _{x\in A}B=\left\{y|\exists x\in Ay\in B\right\}$$
2		nfre1	$$⊢Ⅎx\exists x\in Ay\in B$$
3	2	nfab	$$⊢\underset{\_}{Ⅎ}x\left\{y|\exists x\in Ay\in B\right\}$$
4	1 3	nfcxfr	$$⊢\underset{\_}{Ⅎ}x\bigcup _{x\in A}B$$