"deduction theorem" meaning in English

{
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      "form": "deduction theorems",
      "tags": [
        "plural"
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      "expansion": "deduction theorem (plural deduction theorems)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      "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.",
          "type": "example"
        }
      ],
      "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"
        }
      ],
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        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
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      ],
      "wikipedia": [
        "deduction theorem"
      ]
    }
  ],
  "word": "deduction theorem"
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    {
      "form": "deduction theorems",
      "tags": [
        "plural"
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  "pos": "noun",
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    {
      "word": "conditional proof"
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        {
          "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.",
          "type": "example"
        }
      ],
      "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."
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      "links": [
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          "logic",
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          "inference",
          "inference"
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          "turnstile",
          "turnstile"
        ]
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      "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."
      ],
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        "deduction theorem"
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  "word": "deduction theorem"
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