Is the minimal conjunctive normal form for positive formula unique? If so, how do you calculate it?

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I am considering positive Boolean formulas (no negations). Take for example $A$. Here are two of its positive conjunctive normal forms.

$$A$$ $$A \land (A \lor B)$$

The minimal example is $A$.

Does every positive boolean formula have a unique minimal conjunctive normal form? If so, how does one calculate it?

(I conjecture that you can do so by finding a positive conjuctive normal form, and then pruning any terms that are implied by other terms (for example, $A \lor B$ is implied by the previous term $A$, so it gives no additional information in a conjuction). I don't know how to prove that this is correct, if it is so. (It is also not very efficient.))