Theorem nfra2w

Description: Similar to Lemma 24 of Monk2 p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD . Version of nfra2 with a disjoint variable condition, which does not require ax-13 . (Contributed by Alan Sare, 31-Dec-2011) (Revised by Gino Giotto, 10-Jan-2024)

	Ref	Expression
Assertion	nfra2w	$$⊢Ⅎy\forall x\in A\forall y\in B\phi$$

Proof

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