Since entropy is a state function so it doesn't depends on the path followed. So will the entropy change be equal if a state change be first brought about reversibly and then irreversibly.
If the initial and final states of systems are the same for both reversible and irreversible process, the entropy change for the systems will be the same.
But the entropy change for the surrounding will not be the same, as the final states will be different. The surrounding for the irreversible process will end with higher entropy.
Therefore the total entropy change is zero for reversible processes, but positive for irreversible ones.
The irreversibility condition applies not only to system-surrounding interactions, but for system internal processes as well.