Group Product Inverse Operation with Identity

Theorem
Let $\struct {G, \circ}$ be a group whose identity is $e$.

Let $\oplus: G \times G \to G$ be the product inverse of $\circ$ on $G$.

Then:
 * $\forall x, y \in G: e \oplus \paren {x \oplus y} = y \oplus x$