The proof of invertendo from $\dfrac{a}{b} = \dfrac{c}{d}$ uses the step—

Starting from $\dfrac{a}{b}=\dfrac{c}{d}$, cross-multiplying (multiplying by $bd$) gives $ad=bc$. Dividing this through by $ac$ isolates the terms as $\dfrac{d}{c}=\dfrac{b}{a}$, which is exactly the invertendo relation.