Gruppe/Eindeutige Existenz des Inversen/Fakt/Beweis

Beweis

Sei

{}x\circ y=y\circ x=e\,

und

{}x\circ z=z\circ x=e\,.

Dann ist

{}y=y\circ e=y\circ (x\circ z)=(y\circ x)\circ z=e\circ z=z\,.

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