# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 69: The Deduction Theorem

December 20, 2016

Posted by on In logic, the **deduction theorem** states that where are formulas and is a set of assumptions or axioms, the implication is deducible from if and only if is deducible from . The statement is intuitive, but wasn’t formally proven until 1930.

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