{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn **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.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "inventory": [
      "MGE1ANSF1X"
    ],
    "kind": "concept",
    "name": "Material implication (rule of inference)",
    "same_as": {
      "wikidata": "Q6786560",
      "wikipedia": "Material implication (rule of inference)"
    },
    "sources": [
      {
        "locator": "Material implication (rule of inference)",
        "mention": "wikipedia://en/244516",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:244516@r1364844009"
      }
    ],
    "tag": "64VXCK6M73"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/64VXCK6M73/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/64VXCK6M73.md",
  "msc": null,
  "name": "Material implication (rule of inference)",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/64V/64VXCK6M73.md",
  "status": null,
  "tag": "64VXCK6M73",
  "uri": "m2://64VXCK6M73",
  "url": "https://math2.tamnd.com/wiki/material-implication-rule-of-inference/",
  "writing": {
    "tag": "64VXCK6M73",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}