  We show that under variation of moduli fields $\phi$ the first law of black
hole thermodynamics becomes $dM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq +
\chi dp - \Sigma d\phi$, where $\Sigma$ are the scalar charges. We also show
that the ADM mass is extremized at fixed $A$, $J$, $(p,q)$ when the moduli
fields take the fixed value $\phi_{\rm fix}(p,q)$ which depend only on electric
and magnetic charges. It follows that the least mass of any black hole with
fixed conserved electric and magnetic charges is given by the mass of the
double-extreme black hole with these charges. Our work allows us to interpret
the previously established result that for all extreme black holes the moduli
fields at the horizon take a value $\phi= \phi_{\rm fix}(p,q)$ depending only
on the electric and magnetic conserved charges: $ \phi_{\rm fix}(p,q)$ is such
that the scalar charges $\Sigma ( \phi_{\rm fix}, (p,q))=0$.
