---
tag: 64VXCK6M73
kind: concept
name: Material implication (rule of inference)
sources:
  - wikipedia: en:244516@r1364844009
    locator: Material implication (rule of inference)
    note: adopted
    mention: wikipedia://en/244516
    sections: [Summary]
same_as:
  wikidata: Q6786560
  wikipedia: Material implication (rule of inference)
inventory: [MGE1ANSF1X]
---

## Summary

In **classical** [[propositional logic|09K9MWD2QQ]], **material implication** is a valid rule of replacement that allows a [[conditional statement|0NMG7W7Q11]] to be replaced by a [[disjunction|0F72FK8EKB]] in which the antecedent is [[negated|029JBBF693]]. The rule states that *P implies Q* is [[logically equivalent|06GYGS41JK]] to *not-$P$ or $Q$* and that either form can replace the other in logical proofs. In other words, if $P$ is true, then $Q$ must also be true, while if $Q$ is not true, then $P$ cannot be true either; additionally, when $P$ is not true, $Q$ may be either true or false.