Conditional expectation of function of two independent random variables

Question

Let $X,Y$ two real independent random variables. I need to compute $$\mathbb E[e^\frac{X}{Y}|Y]$$ which as we know is a measurable function of $Y$. Now, for every $y$ fixed I am able to compute $$\mathbb E[e^\frac{X}{y}]=\phi(y)$$ which is a function of $y$. Now one would expect that, by independence of $X$ and $Y$, $$\mathbb E[e^\frac{X}{Y}|Y]=\phi(Y)$$ but I haven't found any property that says that for the conditional expectation. Is there any theorem that I could apply?