Theorem nfra2

Description: Similar to Lemma 24 of Monk2 p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD . Contributed by Alan Sare 31-Dec-2011. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfra2w when possible. (Contributed by NM, 31-Dec-2011) (New usage is discouraged.)

	Ref	Expression
Assertion	nfra2	⊢ Ⅎ 𝑦 ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfcv	⊢ Ⅎ 𝑦 𝐴
2		nfra1	⊢ Ⅎ 𝑦 ∀ 𝑦 ∈ 𝐵 𝜑
3	1 2	nfral	⊢ Ⅎ 𝑦 ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐵 𝜑