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Deduction Theorem

A metatheorem in mathematical logic also known under the name "conditional proof." It states that if the sentential formula B can be derived from the set of sentential formulas A_1,...,A_n, then the sentential formula A_n==>B can be derived from A_1,...,A_(n-1).

In a less formal setting, this means that if a thesis S can be proven under the hypotheses U,V, then one can prove that V implies S under hypothesis U.

See also

Deducible, Deduction, Sentential Formula

This entry contributed by Margherita Barile

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References

Kleene, S. C. "The Deduction Theorem." §21 in Introduction to Metamathematics. Princeton, NJ: Van Nostrand, pp. 90-94, 1964.Monk, D. J. Mathematical Logic. New York: Springer-Verlag, p. 118, 1976.Robbin, J. W. "The Deduction Theorem." §21 in Mathematical Logic. New York: W. A. Benjamin, pp. 16-20, 1969.Shoenfield, J. R. "The Deduction Theorem." §3.3 in Mathematical Logic. Reading, MA: Addison-Wesley, pp. 33-34, 1967.

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Deduction Theorem

Cite this as:

Barile, Margherita. "Deduction Theorem." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/DeductionTheorem.html

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