{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\n**Biconditional elimination** is the name of two valid rules of inference of propositional logic. It allows for one to infer a [[conditional|0NMG7W7Q11]] from a biconditional. If $P \\leftrightarrow Q$ is true, then one may infer that $P \\to Q$ is true, and also that $Q \\to P$ is true. For example, if it's true that I'm breathing if and only if I'm alive, then it's true that if I'm breathing, I'm alive; likewise, it's true that if I'm alive, I'm breathing. The rules can be stated formally as:\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "inventory": [
      "T3AFEXWZDT"
    ],
    "kind": "concept",
    "name": "Biconditional elimination",
    "same_as": {
      "wikidata": "Q4903712",
      "wikipedia": "Biconditional elimination"
    },
    "sources": [
      {
        "locator": "Biconditional elimination",
        "mention": "wikipedia://en/4287",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:4287@r1201988021"
      }
    ],
    "tag": "XDABNSBY2X"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/XDABNSBY2X/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/XDABNSBY2X.md",
  "msc": null,
  "name": "Biconditional elimination",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/XDA/XDABNSBY2X.md",
  "status": null,
  "tag": "XDABNSBY2X",
  "uri": "m2://XDABNSBY2X",
  "url": "https://math2.tamnd.com/wiki/biconditional-elimination/",
  "writing": {
    "tag": "XDABNSBY2X",
    "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
      }
    ]
  }
}