Let $A$ be an integral domain and $a$ an embedded point. So it is given by a non-unit $f$. Let consider the support $\operatorname{Supp} f$ (defined via $\operatorname{Supp} f = \{p \in SpecA | f_p \neq 0 $ in $A_p \}$).
My question refers to a conclusion here: If $A$ is reduced, Spec $A$ has no embedded points
Why $\operatorname{Supp} f\not \supset V(f)$ imply that $\operatorname{Supp} f$ can't be an irreducible component?