Identity is only Idempotent Cancellable Element
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|\(\ds x \circ x\)||\(=\)||\(\ds x\)||$x$ is idempotent|
|\(\ds \)||\(=\)||\(\ds x \circ e_S\)||Definition of Identity Element|
So $x \circ x = x \circ e_S$.
But because $x$ is also by hypothesis cancellable, it follows that $x = e_S$.