I am asked to prove whether or not the following distribution (extreme value distribution) is part of the exponential family:
$$ f_Y(y;\mu,\phi)=\frac{1}{\phi}\exp[-\frac{y-\mu}{\phi}+\exp(-\frac{y-\mu}{\phi})]$$
My definition of the exponential family is the following:
I have tried rewriting the density function and obtained: $$f_Y(y;\mu,\phi)=\exp \left[\log\frac{1}{\phi}-\frac{y}{\phi}+\frac{\mu}{\phi}-\exp\left(\frac{-y+\mu}{\phi}\right)\right]$$ However, at this point I am stuck. How do I get the density function into the form of the exponential family distribution from this point? Any help would be very much appreciated!