Theorem nfii1

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

	Ref	Expression
Assertion	nfii1	⊢ Ⅎ 𝑥 ∩ 𝑥 ∈ 𝐴 𝐵

Proof

Step	Hyp	Ref	Expression
1		df-iin	⊢ ∩ 𝑥 ∈ 𝐴 𝐵 = { 𝑦 ∣ ∀ 𝑥 ∈ 𝐴 𝑦 ∈ 𝐵 }
2		nfra1	⊢ 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