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	|- F/ y A. x e. A A. y e. B ph

Proof

Step	Hyp	Ref	Expression
1		nfcv	|- F/_ y A
2		nfra1	|- F/ y A. y e. B ph
3	1 2	nfralw	|- F/ y A. x e. A A. y e. B ph