Simply Typed Lambda Calculus question - Beta Reduction

[semiflex]

Homework Statement

Under the assumption that BETA is a closed term show that (λx.α)(β) and α[x→β] are logically equivalent.

Homework Equations

I'm sure I have to use β-reduction but I'm not sure how in this case:

⊢(λx.x)(β→α[x→β]

The Attempt at a Solution

 

[verty]

What does α[x→β] mean?