Definition:Conditional/Formal Implication

Definition
Formal implication is a usage of an implication in which it is necessary for there to be a formal connection between the antecedent and the consequent in order for the implication to have any semantic meaning.

Also see

 * Rule of Material Implication, which defines a mode of usage of a conditional statement which allows for there to be no direct physical or linguistic connection between the antecedent and the consequent.