Bounded waiting implies progress, and progress implies mutual exclusion.
Bounded waiting says that after certain no. of processes executed the waiting process will be executed.
Progress says that if a process isn't inside critical section then it shouldn't stop other process while it is going into critical section .
combining both of above we get true since a process is waiting until it's bounded waiting time it doesn't interrupt other processes.
Mutual Exclusion says that no 2 processes should be inside critical section at atime. Hence if there is progress then mutual Exclusion is guaranteed.
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