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===Exemplary proofs===

===Exemplary proofs===

With the meagre means afforded by the axioms and theorems given so far, it is already possible to prove a multitude of much more complex theorems.  A couple of all-time favorites are given next.

With the meagre utilities of the axioms and theorems set down so far, it is already possible to prove a multitude of much more complex theorems.  A couple of all-time favorites are given next.

====Peirce's law====

====Peirce's law====

This section presents a proof of Peirce's law, commonly written:

This section presents a proof of Peirce's law, commonly written:

:* [[p ⇒ q] ⇒ p] ⇒ p

 

: <math>((p \Rightarrow q) \Rightarrow p) \Rightarrow p</math>

The first order of business is present the statement as it  appears in the so-called ''existential interpretation'' of Peirce's own ''logical graphs''.  Here is the statement of Peirce's law, as rendered under the existential interpretation into (the topological dual forms of) Peirce's logical graphs:

The first order of business is present the statement as it  appears in the so-called ''existential interpretation'' of Peirce's own ''logical graphs''.  Here is the statement of Peirce's law, as rendered under the existential interpretation into (the topological dual forms of) Peirce's logical graphs: