Theorem nfra2

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

	Ref	Expression
Assertion	nfra2	$$⊢Ⅎy\forall x\in A\forall y\in B\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}yA$$
2		nfra1	$$⊢Ⅎy\forall y\in B\phi$$
3	1 2	nfral	$$⊢Ⅎy\forall x\in A\forall y\in B\phi$$