Theorem nfiu1OLD

Description: Obsolete version of nfiu1 as of 14-May-2025. (Contributed by NM, 12-Oct-2003) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	nfiu1OLD	$$⊢\underset{\_}{Ⅎ}x\bigcup _{x\in A}B$$

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	$$⊢\underset{\_}{Ⅎ}x\bigcup _{x\in A}B$$