Material implication

Transformation rules
Propositional calculus
Rules of inference Modus ponens Modus tollens Modus ponendo tollens Biconditional introduction Biconditional elimination Conjunction introduction Simplification Disjunction introduction Disjunction elimination Disjunctive syllogism Hypothetical syllogism Constructive dilemma Destructive dilemma Absorption Rules of replacement Associativity Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology
Predicate logic
Universal generalization Universal instantiation Existential generalization Existential instantiation

For the logical connective of the same name see Material conditional.

In propositional logic, material implication is a rule of replacement that states that P implies Q is logically equivalent to not P or Q.
In formal notation it becomes:

$P\rightarrow Q \iff \neg P\or Q$

Examples

If it is December 25, it is Christmas. Thus, it is either not December 25 or Christmas.

Since it has to be the case that it is Christmas on December 25, the current day is either not December 25 (Christmas) or not Christmas.