If I had a Binding Band and a Grip Claw out in a Double Battle, would both the items affect the same trap?

Here's a hypothetical example of what I mean:

1. On my side in a Double Battle I have:
~A Vulpix with Fire Spin holding a Binding Band
~A Sneasel holding a Grip Claw

2. The hypothetical Vulpix hits an opponent with Fire Spin

Will the Fire Spin be guaranteed to last 5 turns thanks to the Ally's Grip Claw?
Or will it only be affected by the Binding Band?