Denying the Antecedent

Fallacy
Let $p \implies q$ be a conditional statement.

Let its antecedent $p$ be false.

Then it is a fallacy to assert that the consequent $q$ is also necessarily false.

That is:
 * $p \implies q, \neg p \not \vdash \neg q$

Also see

 * Affirming the Consequent