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Metamath Proof Explorer

Theorem nfii1

Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by NM, 15-Oct-2003)

Ref Expression
Assertion nfii1 ⊢ Ⅎ _ x ⋂ x ∈ A B

Proof

Step Hyp Ref Expression
1 df-iin ⊢ ⋂ x ∈ A B = y | ∀ x ∈ A y ∈ B
2 nfra1 ⊢ Ⅎ x ∀ x ∈ A y ∈ B
3 2 nfab ⊢ Ⅎ _ x y | ∀ x ∈ A y ∈ B
4 1 3 nfcxfr ⊢ Ⅎ _ x ⋂ x ∈ A B