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A set of inference rules for propositional logic
Our propositional inference rules
Abbreviation Name If you know all of then you can infer
Intro and-introduction
Elim and-elimination (left)
and-elimination (right)
Intro or-introduction (left)
or-introduction (right)
Elim or-elimination
Intro if-introduction , , ,
Elim if-elimination (modus ponens)
Intro false-introduction
Elim false-elimination
RAA reductio ad absurdum (v. 1)
reductio ad absurdum (v. 2)
Intro negation-introduction
Elim negation-elimination
CaseElim case-elimination (left)
case-elimination (right)

As usual, , , , are meta-variables standing for any WFF.

This is by no means the only possible inference system for propositional logic.

This set of inference rules is based upon Discrete Mathematics with a Computer by Hall and O'Donnell (Springer, 2000) and The Beseme Project .

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Source:  OpenStax, Intro to logic. OpenStax CNX. Jan 29, 2008 Download for free at http://cnx.org/content/col10154/1.20
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