Semiconductor intrinsic Fermi Level? Bandgap Energy?

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kidsasd987
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http://ecee.colorado.edu/~bart/book/book/chapter2/ch2_6.htm#2_6_2
equation (2.6.24)

eq2_6_24.gif


we have this equation for fermi level, but I wonder how this works though?
In the lecture, we assumed Ec=Eg and Ev=0 to get E_gap/2.

but I wonder how (Ec+Ev)/2 actually gives E_gap/2 instead of Ec-Ev=Eg
 
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It was a stupid question. sorry.