# Today I Learned

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

## 131: Pierce’s Law

In classical logic, Pierce’s Law is the property that

$((P \rightarrow Q) \rightarrow P) \rightarrow P$.

Proof:

$(P \rightarrow Q) \rightarrow P$

$\Downarrow$

$\overline{P \rightarrow Q} \vee P$

$\Downarrow$

$\overline{\overline{P} \vee Q} \vee P$

$\Downarrow$

$(P \wedge \overline{Q}) \vee P$

$\Downarrow$

$(P \wedge \overline{Q}) \vee (P \wedge 1)$

$\Downarrow$

$P$