Theorem nfiu1

Description: Bound-variable hypothesis builder for indexed union. (Contributed by NM, 12-Oct-2003) Avoid ax-11 , ax-12 . (Revised by SN, 14-May-2025)

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

Proof

Step	Hyp	Ref	Expression
1		eliun	$$⊢y\in \bigcup _{x\in A}B\leftrightarrow \exists x\in Ay\in B$$
2		nfre1	$$⊢Ⅎx\exists x\in Ay\in B$$
3	1 2	nfxfr	$$⊢Ⅎxy\in \bigcup _{x\in A}B$$
4	3	nfci	$$⊢\underset{\_}{Ⅎ}x\bigcup _{x\in A}B$$