Form 1 says that "For any relation R, there is a function with ".

Assume Form1.

We define a relation R such that , where a choice function C is defined as such that is an element of . Since and is not empty, the existence of choice function C is followed from a Form1, satisfying the Form 2.

Conversely, assume Form 2.

Let ; let .

Now, we have and for each i, .

That means, there exists a choice function such that we retrieve for each .

Now, consider any relation R. The existence of a choice function C provides us with a mapping from to .

Then, , i.e., . Thus, .