Metamath Proof Explorer

Theorem nfii1

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

Ref Expression
Assertion nfii1 
|- F/_ x |^|_ x e. A B

Proof

Step Hyp Ref Expression
1 df-iin 
 |-  |^|_ x e. A B = { y | A. x e. A y e. B }
2 nfra1 
 |-  F/ x A. x e. A y e. B
3 2 nfab 
 |-  F/_ x { y | A. x e. A y e. B }
4 1 3 nfcxfr 
 |-  F/_ x |^|_ x e. A B