Originally Posted by

**namelessguy** I am given two forms of the axiom of choice, and I need to show that they are equivalent. Can someone help?

Form 1: $\displaystyle (\forall R)$$\displaystyle (R$ a relation $\displaystyle \rightarrow (\exists f)$$\displaystyle [f$ a function and $\displaystyle f \subseteq R$ and $\displaystyle domf= domR])$

Form 2: $\displaystyle (\forall X)$[If $\displaystyle \forall y \in X$, y is not equal the empty set, then $\displaystyle \prod X$ is not equal the empty set.

Where $\displaystyle \prod X$ is the Cartesian product defined as the set of functions f with dom f=X and for all y in X, f(y) is in y.