I have the following question: 

>Let $A$ be an Artin algebra. Let $S_1$ and $S_2$ be simple modules in $\text{mod}(A)$ and let $P(S_1)$ be the projective cover of $S_1$. Let $f: P(S_1) \rightarrow S_2$ be module homomorphism with $f \neq 0$. Then $S_1 \cong S_2$.

Any help is highly appreciated!