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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 $H$.

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Group, Def/Group homomorphism

The following statements and definitions rely on the material of this page: Def/Conjugate

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