Exponential of Sum/Real Numbers/Corollary

Corollary to Exponent of Sum: Real Numbers
Let $x, y \in \R$ be real numbers.

Let $\exp x$ be the exponential of $x$.

Then:
 * $\exp \left({x - y}\right) = \dfrac {\exp x} {\exp y}$

Proof
By Exponent of Sum: Real Numbers:


 * $\exp \left({x - y}\right) = \exp x \exp \left({- y}\right)$

By Reciprocal of Complex Exponential:


 * $\dfrac 1 {\exp y} = \exp \left({- y}\right)$

Combining these two, we obtain the result:


 * $\exp \left({x - y}\right) = \dfrac {\exp x} {\exp y}$