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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 ⊢ Ⅎ y ∀ x ∈ A ∀ y ∈ B φ

Proof

Step Hyp Ref Expression
1 nfcv ⊢ Ⅎ _ y A
2 nfra1 ⊢ Ⅎ y ∀ y ∈ B φ
3 1 2 nfral ⊢ Ⅎ y ∀ x ∈ A ∀ y ∈ B φ