Metamath Proof Explorer


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