Group/Homomorphism theorem/Kernel of the induced homomorphism/Exercise

Let $G,H,$ and $F$ be groups, and let $\phi :G\to H$ and $\psi :G\to F$ denote group homomorphisms. Suppose that $\psi$ is surjective and that $\mathrm{kern}\psi \subseteq \mathrm{kern}\phi$ holds. Determine the kernel of the induced homomorphism

$\tilde{\phi }:F⟶H.$

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