Rule of Material Implication

Theorem
The rule of material implication is a valid deduction sequent in propositional logic:

Formulation 2
That is:


 * statement $p$ implies statement $q$

is logically equivalent to:


 * statement $p$ is true or statement $q$ is false

Also known as
This rule is sometimes seen referred to as the definition of material implication, as some sources use this rule as a definition of the conditional, so as to justify its semantics.

Also see
The following are related argument forms:
 * Modus Ponendo Tollens
 * Modus Tollendo Tollens