# Today I Learned

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

## 69: The Deduction Theorem

In logic, the deduction theorem states that where $A, B$ are formulas and $\Delta$ is a set of assumptions or axioms, the implication $A \rightarrow B$ is deducible from $\Delta$ if and only if $B$ is deducible from $\Delta \bigcup \{A\}$. The statement is intuitive, but wasn’t formally proven until 1930.