Assume $A \subset B$ and $A \neq \emptyset$. Prove $B \neq \emptyset$.

Question

I have an exercise stating

Assume $A \subset B$ and $A \neq \emptyset$. Prove $B \neq \emptyset$.

Is my proof adequate, or have I missed anything out? Any tips would be greatly appreciated as I am self taught new to proof writing.

Proof : As $A \neq \emptyset$ , $ \exists a , (a \in A)$. Also, as $A \subset B$ , $\forall a \in A, (a \in B)$. From this we get $\exists a , (a \in B)$. Therefore, $B \neq \emptyset$

Answer 1

Your proof is correct and well-presented. Good job!

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Mostly posting this so this question can be finally considered to have an answer and thus be removed from the unanswered queue. Made it Community Wiki since I have nothing much of substance to add.