Metamath Proof Explorer

Theorem nfiu1

Description: Bound-variable hypothesis builder for indexed union. (Contributed by NM, 12-Oct-2003)

Ref Expression
Assertion nfiu1 
|- F/_ x U_ x e. A B

Proof

Step Hyp Ref Expression
1 df-iun 
 |-  U_ x e. A B = { y | E. x e. A y e. B }
2 nfre1 
 |-  F/ x E. x e. A y e. B
3 2 nfab 
 |-  F/_ x { y | E. x e. A y e. B }
4 1 3 nfcxfr 
 |-  F/_ x U_ x e. A B