local_bh_disable vs. local_irq_disable: hierarchical?

My straightforward question: If code has called local_irq_disable, does
this guarantee that a bottom half handler cannot run?

I'm looking for a statement on semantics. I've tried to hunt
documentation in many forms. None of them imply that disabling irqs would also disable bottom halves. It might just be me, but I have a strong sense that disabling interrupts is a stronger statement than disabling bottom halves.

However I don't want to trust my instincts for this. I am looking for a
clear statement on the Linux definitions. And I am not asking this question just to satisfy some curiosity -- there is an underlying problem I'm hoping to put to rest.

Thanks!
-- Ethan