There are 2 ways of saying a function, , is uniformly continuous

A. For every , there exists a such that

whenever and

B. For every , there exists a such that

whenever and

Prove f satisfies A if and only if it satisfies B

This is a confusing proposition. I think if f satisfies B, then it obviously satisfies A, but I could be mistaken.

And if it satisfies A, how do I go about demonstrating B?

Thanks in advance for the help