Fugacity and pressure are numerically equal, when the gas is

We know the concept of fugacity is originated from the equation $$d{\mu _i} = pdv - sdT$$    for an pure gas.
Under constant temperature and assuming an ideal gas we can write this as $$d\mu = RTdlnP$$    and for an real gas the same equation is assumed keeping all the non-ideality in the term fugacity and written as $$d\mu = RTdlnf$$
So, we can say for an ideal gas $$f = p.$$