Is there a name for this type of logical fallacy? Consider a statement of the form: $A$ implies $B$, where $A$ and $B$ are true, but $B$ is not implied by $A$. 
Example: As $3$ is odd, $3$ is prime. 
In this case, it is true that $3$ is odd, and that $3$ is prime, but the implication is false. If $9$ had been used instead of $3$, the first statement would be true, but the second wouldn't, in which case it is clear that the implication is false.

Is there a name for this sort of logical fallacy?


Others have said this is not a fallacy, and that is true in the logics we are used to using in mathematics, but perhaps not in the logics used in natural language or, say, the law.  For example, Relevance Logic is designed to disallow this sort of thing.
