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Repeat "let" and/or "be"? Example: Let A be a line and (let?) B (be?) a plane

While fixing my notation in a research article, I want to write something like this: Let A be a line and (let) B (be) a plane. … Question: Do I have to write the second let and be or can I omit one or both of them? (The context is a research article in mathematics, if this should matter. …
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