it is defined that "$deadlock\rightarrow \overline{progression}$"
$\Rightarrow$ $\overline{deadlock}+\overline{progress}$
$\Rightarrow$ $\overline{deadlock}+\overline{1}$ // since system is progressive
$\Rightarrow$ $\overline{deadlock}$ //no deadlock
this means that meeting progress implies system is deadlock free