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