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State/Homomorphic images of subgroups are subgroups
Proposition: (Homomorphic images of subgroups are subgroups) Suppose that $G$ and $H$ are groups, and $\phi \colon G \rightarrow H$ is a homomorphism. Let $L$ be a subgroup of $G$. Then $\phi(L)$ is a subgroup of $H$.
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