Recognizer to check if the language of a Turing machine contains a finite subset

Let $$B = \{ 123 \}$$.

Note that $$B$$ is finite.

Let $$L = \left \{ \left\langle M \right\rangle | M \text{ is a Turing machine such that } B \subseteq L(M) \right\}$$.

Is it sufficient to show that $$L$$ is recognizable by checking if $$M$$ accepts on input $$123$$, and therefore $$\left\langle M \right\rangle \in L$$?

$$\langle M \rangle \in L \Longleftrightarrow B\subseteq L(M) \Longleftrightarrow M\text{ accepts all strings in }B \Longleftrightarrow M\text{ accepts }123$$.