In Logic the term ‘antecedent’ is used to designated the part of a conditional (or hypothetical) proposition that follows the world ‘if’.
A conditional proposition is any proposition that asserts “If subject term, then predicate term.”
In conditional propositions the antecedent term asserts a sufficient condition for the predicate term’s existence or occurrence. That is, if the sufficient condition is met, then it must be the case that the event or act asserted in the predicate will be true.
For example in the statement “If you get an A on the final exam, then you will pass the class,” the antecedent term (“you get an A on the final exam”) is asserted to be a sufficient condition (it is the minimum that must occur) for passing the class.
Following this example we can clearly see that there is only one condition when a conditional statement will be false: when the fact of the antecedent is met, but the consequent does not follow (e.g., you got an A on the final, but did not pass the class).