"deduction theorem" meaning in English

{
  "forms": [
    {
      "form": "deduction theorems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "deduction theorem (plural deduction theorems)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "The deduction theorem reveals the relationship between logical entailment and material implication: it allows to one to \"pack\" or \"record\" an inference into a tautology, and conversely, to \"unpack\" or \"play back\" a tautology as an inference process."
        }
      ],
      "glosses": [
        "A procedure for \"discharging\" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form P,A⊢C to an inference of the form P⊢A→C or vice versa, where ⊢ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory."
      ],
      "id": "en-deduction_theorem-en-noun-FSD2lVus",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "inference",
          "inference"
        ],
        [
          "antecedents",
          "antecedents"
        ],
        [
          "turnstile",
          "turnstile"
        ]
      ],
      "raw_glosses": [
        "(logic) A procedure for \"discharging\" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form P,A⊢C to an inference of the form P⊢A→C or vice versa, where ⊢ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory."
      ],
      "related": [
        {
          "word": "conditional proof"
        }
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "deduction theorem"
      ]
    }
  ],
  "word": "deduction theorem"
}

{
  "forms": [
    {
      "form": "deduction theorems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "deduction theorem (plural deduction theorems)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "conditional proof"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Logic"
      ],
      "examples": [
        {
          "text": "The deduction theorem reveals the relationship between logical entailment and material implication: it allows to one to \"pack\" or \"record\" an inference into a tautology, and conversely, to \"unpack\" or \"play back\" a tautology as an inference process."
        }
      ],
      "glosses": [
        "A procedure for \"discharging\" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form P,A⊢C to an inference of the form P⊢A→C or vice versa, where ⊢ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "inference",
          "inference"
        ],
        [
          "antecedents",
          "antecedents"
        ],
        [
          "turnstile",
          "turnstile"
        ]
      ],
      "raw_glosses": [
        "(logic) A procedure for \"discharging\" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form P,A⊢C to an inference of the form P⊢A→C or vice versa, where ⊢ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "deduction theorem"
      ]
    }
  ],
  "word": "deduction theorem"
}