Deduction Theorem
المؤلف:
Kleene, S. C
المصدر:
"The Deduction Theorem." §21 in Introduction to Metamathematics. Princeton, NJ: Van Nostrand
الجزء والصفحة:
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23-1-2022
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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 
can be derived from the set of sentential formulas 
, then the sentential formula 
can be derived from 
.
In a less formal setting, this means that if a thesis 
can be proven under the hypotheses 
, then one can prove that 
implies 
under hypothesis 
.
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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