Suppose that $X$ and $Y$ are discrete random variables with PMFs $p_X$ and $p_Y$. The conditional probability mass function of $X$ given that $Y = y$ is often denoted $p_{X \mid Y}(x \mid y)$ (assuming that $p_Y(y) > 0$). However, is there any reason not to use the notation $p_{X \mid Y = y}(x)$ instead? I find the latter notation to be much more clear.
Similarly, if $X$ and $Y$ are jointly continuous random variables with PDFs $f_X$ and $f_Y$, the conditional probability density of $X$ given that $Y = y$ is often denoted $f_{X|Y}(x \mid y)$ (assuming that $f_Y(y) > 0$). Is there any reason not to use the notation $f_{X \mid Y = y}(x)$ instead? It seems more clear, but perhaps I am missing some subtle point.
Are there any textbooks which use the notation $f_{X \mid Y=y}(x)$?