na.numerical analysis - A question about the lagrangian $L(x,lambda, nu)$ in the dual function in Convex Optimization

Hi.
My question is probably very simple to some of you that have experience in Convex Optimization.
The dual function is defined as the infimum of the lagrangian $L(x,lambda, nu)$ over all $x $ in the domain. The lagrangian is:
$f_0(x)+sum lambda_i f_i(x)+sum nu_i h_i(x)$

My question is, if $x $ is in the domain, it satisfies the equality constraints $h_i(x)$ and in that case, $h_i(x)=0$. So why do we even have to mention the equality constraints if they zero-out anyway?

Thanks a lot, I hope I wrote my question clearly.