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If ${\left(e^{-tA}\right)}_{t>0}$ is a strongly continuous and contractive semigroup on a complex Banach space $B$, then $-{(-A)}^{\alpha }$, $0<\alpha <1$, generates a holomorphic semigroup on $B$. This was proved by K. Yosida in [7]. Using similar techniques, we present a class $H$ of Bernstein functions such that for all $f\in H$, the operator $-f(-A)$ generates a holomorphic semigroup.