Theorem nfra2w

Description: Similar to Lemma 24 of Monk2 p. 114, except that quantification is restricted. Once derived from hbra2VD . Version of nfra2 with a disjoint variable condition not requiring ax-13 . (Contributed by Alan Sare, 31-Dec-2011) Reduce axiom usage. (Revised by Gino Giotto, 24-Sep-2024) (Proof shortened by Wolf Lammen, 3-Jan-2025)

	Ref	Expression
Assertion	nfra2w	|- F/ y A. x e. A A. y e. B ph

Proof

Step	Hyp	Ref	Expression
1		r2al	|- ( A. x e. A A. y e. B ph <-> A. x A. y ( ( x e. A /\ y e. B ) -> ph ) )
2		nfa2	|- F/ y A. x A. y ( ( x e. A /\ y e. B ) -> ph )
3	1 2	nfxfr	|- F/ y A. x e. A A. y e. B ph