Theorem nfiu1

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

	Ref	Expression
Assertion	nfiu1	⊢ Ⅎ 𝑥 ∪ 𝑥 ∈ 𝐴 𝐵

Proof

Step	Hyp	Ref	Expression
1		df-iun	⊢ ∪ 𝑥 ∈ 𝐴 𝐵 = { 𝑦 ∣ ∃ 𝑥 ∈ 𝐴 𝑦 ∈ 𝐵 }
2		nfre1	⊢ Ⅎ 𝑥 ∃ 𝑥 ∈ 𝐴 𝑦 ∈ 𝐵
3	2	nfab	⊢ Ⅎ 𝑥 { 𝑦 ∣ ∃ 𝑥 ∈ 𝐴 𝑦 ∈ 𝐵 }
4	1 3	nfcxfr	⊢ Ⅎ 𝑥 ∪ 𝑥 ∈ 𝐴 𝐵