Prove that \( \mathrm{A}^{\mathrm{C}}-\mathrm{B}^{\mathrm{C}}=\mathrm{B}-\mathrm{A} \).

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Prove that \( \mathrm{A}^{\mathrm{C}}-\mathrm{B}^{\mathrm{C}}=\mathrm{B}-\mathrm{A} \).
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