Propositional calculus implies standard axioms

In order to avoid duplicating a lot of the work in Principia Mathematica propositional logic, we'll just import Interface:Classical propositional calculus. Since Principia Mathematica propositional logic proves that interface from the Principia axioms, this is equivalent to importing the Principia axioms.

 import (CLASSICAL Interface:Classical_propositional_calculus ) var (formula p q r) 

The first axiom, Simp, is called  in Interface:Classical propositional calculus.  thm (Simp  (p → (q → p)) ( p q AntecedentIntroduction )) 

The second axiom, Frege, is one direction of  from Interface:Classical propositional calculus.

 thm (Frege  ((p → (q → r)) → ((p → q) → (p → r))) ( p q r AntecedentDistribution eliminateBiconditionalReverse )) 

The third axiom, Transp, is one direction of  from Interface:Classical propositional calculus.  thm (Transp  (((¬ p) → (¬ q)) → (q → p)) ( q p Transposition eliminateBiconditionalForward )) 

The inference rule,, is the same in the two sets of axioms (and has the same name), so we don't need to do anything.

 export (STANDARD Interface:Standard_axioms_of_propositional_logic ) 