How are the formulae of isochoric processes used in adiabatic processes?

We have the formula for an isochoric process:


$c\_V = \frac{\mathrm{d}E}{\mathrm{d}T}$ at constant volume.


$c\_V=$ molar heat capacity at constant volume.


But it's given for adiabatic changes,
$$\delta E=c\_V\cdot \Delta T=W$$


How is this an equation for an adiabatic process when it's derived from equations of an isochoric process?


Is an adiabatic process also isochoric?


Where am I going wrong?


