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

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